MTH 11203Algebra

EXPONENTS PARENTHESES AND THE ORDER OF OPERATIONS

CHAPTER 1 SECTION 9

Learn the Meaning of Exponents

General bn b is called the base n is called the exponentn factors of b(b)(b)(b)(b)hellip(b) = bn

b4 = (b)(b)(b)(b) or bbbbx3 = (x)(x)(x) or xxx

Learning the Meaning of Exponents

Whenever we see a variable or number without an exponent we always assume that the exponent is 1

An exponent refers only to the number or variable that directly precedes it hellip unless parentheses are used to indicate otherwise

-x2 not the same as (-x)2

(-)(x)(x) (-x)(-x)

Learn the Meaning of Exponents

32 3 is called the base 2 is called the exponent2 factors of 3(3)(3) = 9

53

5 is called the base 3 is called the exponent3 factors of 5(5)(5)(5) = 125

17 pg 77) 52 ldquo5 squaredrdquo(5)(5) 5 is the base 2 is the exponent25 ldquo5 to the second powerrdquo

2 factors of 5

21 pg 77 73 ldquo7 cubedrdquo(7)(7)(7) ldquo7 to the third powerrdquo(49)(7) 3 factors of 7343 7 is the base 3 is the exponent

Exp b3 = bbb ldquob cubedrdquo

Exp x4 = xxxx ldquox to the fourthrdquo

Expamples

28) 53 19) 17

(5)(5)(5) (1)(1)(1)(1)(1)(1)(1)

(25)(5) 1

125

20) 41 37)

(4)

4

Examples

23 3 3 3 3 9

4 4 4 4 4 16

Write as an exponent

a) xyxx = x3y

b) xyzzy = xy2z2

c) 3aabb b = 3a2b3

d) 5xyyyy = 5xy3

e) (4)(4)rrs = 42r2s

f) (5)(5)(5)mmn = 53m2n

Exponential Notation

Exponents refer to the number or variable directly preceding it unless it is in

parenthesis

EXP -x2 only the x will be squared (-)(x)(x)

ldquonegative x squaredrdquo or ldquothe opposite of x squaredrdquo

EXP (-x)2 all will be squared (-x)(-x)

ldquonegative x quantity squaredrdquo

EXP -62 = (-)(6)(6) = -36

EXP (-6)2 = (-6)(-6)= 36

Difference between ndashx2 and (-x)2

30) (-7)2 even neg = pos result

(-7)(-7)

-49

Exp) (-4)4 even neg = pos result

(-4)(-4)(-4)(-4)

(16)(-4)(-4)

(-64)(-4)

256

Examples

exp) -102 exp) (-10)2

(-)(10)(10) (-10)(-10)

-100 100

exp) -43 exp) (-4)3 odd neg = neg result

(-)(4) (4)(4) (-4)(-4)(-4)

-64 (16)(-4)

-64

Examples

exp) (-3)4 exp) -(3)4

even neg = pos result

(-3)(-3)(-3)(-3) (-)(3)(3)(3)(3)

(9)(-3)(-3) (-3)(3)(3)(3)

(-27)(-3) (-9)(3)(3)

81 (-27)(3)

-81

Examples

EXP (-5)2 = (-5)(-5) = 25

EXP -(5)2 = -(5)(5) = -25

EXP -23 = -(2)(2)(2) = -8

EXP (-2)3 = (-2)(-2)(-2) = -8

EXP -24 = -(2)(2)(2)(2) = -16

EXP (-2)4 = (-2)(-2)(-2)(-2) = 16

EXP (-7)2 = (-7)(-7) = 49

EXP (-3)3 = (-3)(-3)(-3) = -27

Difference between ndashx2 and (-x)2

Help using your calculator is on page 70

EXP -102 = -(10)(10) = -100

EXP (-10)2 = (-10)(-10) = 100

EXP -43 = -(4)(4)(4) = -64

EXP (-4)3 = (-4)(-4)(-4) = -64

Calculator

Order of Operation

1 Evaluate within grouping symbols [ ] ( )

innermost parenthesis first

2 Evaluate exponents

3 Multiply or Divide from left to right

4 Add or Subtract from left to right

Please Excuse My Dear Aunt Sally ndash PEMDAS

Remember its multiply or divide add or subtract

Parenthesis can be used to change the order of operations or to clarify the order

EXP 2 + 3 4 = 2 + (3 4) = 2 + 12 = 14

Learning the Order of Operations

Nested Parenthesis is one set inside another

Use the innermost parenthesis first

EXP EXP

Learning the Order of Operations

6[2 3(4 1)]

6[2 3(5)]

6[2 15]

6[17]

102

4[3(6 4) 6]

4[3(2) 6]

4[6 6]

4[1]

4

EXP EXP

Examples

23 2 4 8

3 2 16 8

3 32 8

35 8

27

25 4[ 3 (100 5 )]

5 4[ 3 (100 25)]

5 4[ 3 (4)]

5 4[1]

5 4

1

EXP EXP

Examples

2

2

(14 2) 5(3 2)

(7) 5(1)

7 5(1)

7 5

12

29 72 8 3 5

9 72 8 9 5

9 9 9 5

9 81 5

90 5

85

EXP EXP

Examples

25 18 3

25 18 3

25 6

19

2( 5) 18 3

25 18 3

25 6

31

EXP

Examples

4 3 2

7 5 9

4 3

7

1

2

5 9

3

4 2 = 105

7 15

4 15 60 2 7 14 and

7 15 105 15 7 105

60 14

105 105

46

105

LCD

Examples

Write the following statement as mathematical expressions using parentheses and brackets and then evaluate

Multiply 9 by 6 add 7 to this product Subtract 12 from the sum Divide this difference by 5

[[(9 6) + 7] ndash 12] divide 5

495

EXP

EXP

EXP

Evaluate Expressions Containing Variables

8 7 when 4

8(4) 732 725

x x

2

2 when 9

9 (9)(9) 81x x

2

2 when 9

9 (9)(9) 81x x

EXP

EXP

Evaluate Expressions Containing Variables

2

2 when 6

( 6) ( 6)( 6) 36y y

2

2 when 6

( 6) ( 6)( 6) 36y y

EXP

Evaluate Expressions Containing Variables

2

2

22 3 4 when

3

2 2 4 22 3 4 = 2 3 4

3 3 9 3

2 4 3 2 8 64 = 4 LCD = 9

1 9 1 3 9 3

8 18 10 4 10 364 = =

9 9 9 1 9 9

26 8 or 2

9 9

x x x

EXP

Evaluate Expressions Containing Variables

2

2

2( 7) 3 when 2 and 1

( 1) 2( 2 7) 3

1 2( 2 7) 3

1 2(5) 3

1 10 3

9 3

6

y x x y

HOMEWORK 19

Page 77 ndash 7818 21 29 35 43 57 61 75 79 83 87 95

Learn the Meaning of Exponents

General bn b is called the base n is called the exponentn factors of b(b)(b)(b)(b)hellip(b) = bn

b4 = (b)(b)(b)(b) or bbbbx3 = (x)(x)(x) or xxx

Learning the Meaning of Exponents

Whenever we see a variable or number without an exponent we always assume that the exponent is 1

An exponent refers only to the number or variable that directly precedes it hellip unless parentheses are used to indicate otherwise

-x2 not the same as (-x)2

(-)(x)(x) (-x)(-x)

Learn the Meaning of Exponents

32 3 is called the base 2 is called the exponent2 factors of 3(3)(3) = 9

53

5 is called the base 3 is called the exponent3 factors of 5(5)(5)(5) = 125

17 pg 77) 52 ldquo5 squaredrdquo(5)(5) 5 is the base 2 is the exponent25 ldquo5 to the second powerrdquo

2 factors of 5

21 pg 77 73 ldquo7 cubedrdquo(7)(7)(7) ldquo7 to the third powerrdquo(49)(7) 3 factors of 7343 7 is the base 3 is the exponent

Exp b3 = bbb ldquob cubedrdquo

Exp x4 = xxxx ldquox to the fourthrdquo

Expamples

28) 53 19) 17

(5)(5)(5) (1)(1)(1)(1)(1)(1)(1)

(25)(5) 1

125

20) 41 37)

(4)

4

Examples

23 3 3 3 3 9

4 4 4 4 4 16

Write as an exponent

a) xyxx = x3y

b) xyzzy = xy2z2

c) 3aabb b = 3a2b3

d) 5xyyyy = 5xy3

e) (4)(4)rrs = 42r2s

f) (5)(5)(5)mmn = 53m2n

Exponential Notation

Exponents refer to the number or variable directly preceding it unless it is in

parenthesis

EXP -x2 only the x will be squared (-)(x)(x)

ldquonegative x squaredrdquo or ldquothe opposite of x squaredrdquo

EXP (-x)2 all will be squared (-x)(-x)

ldquonegative x quantity squaredrdquo

EXP -62 = (-)(6)(6) = -36

EXP (-6)2 = (-6)(-6)= 36

Difference between ndashx2 and (-x)2

30) (-7)2 even neg = pos result

(-7)(-7)

-49

Exp) (-4)4 even neg = pos result

(-4)(-4)(-4)(-4)

(16)(-4)(-4)

(-64)(-4)

256

Examples

exp) -102 exp) (-10)2

(-)(10)(10) (-10)(-10)

-100 100

exp) -43 exp) (-4)3 odd neg = neg result

(-)(4) (4)(4) (-4)(-4)(-4)

-64 (16)(-4)

-64

Examples

exp) (-3)4 exp) -(3)4

even neg = pos result

(-3)(-3)(-3)(-3) (-)(3)(3)(3)(3)

(9)(-3)(-3) (-3)(3)(3)(3)

(-27)(-3) (-9)(3)(3)

81 (-27)(3)

-81

Examples

EXP (-5)2 = (-5)(-5) = 25

EXP -(5)2 = -(5)(5) = -25

EXP -23 = -(2)(2)(2) = -8

EXP (-2)3 = (-2)(-2)(-2) = -8

EXP -24 = -(2)(2)(2)(2) = -16

EXP (-2)4 = (-2)(-2)(-2)(-2) = 16

EXP (-7)2 = (-7)(-7) = 49

EXP (-3)3 = (-3)(-3)(-3) = -27

Difference between ndashx2 and (-x)2

Help using your calculator is on page 70

EXP -102 = -(10)(10) = -100

EXP (-10)2 = (-10)(-10) = 100

EXP -43 = -(4)(4)(4) = -64

EXP (-4)3 = (-4)(-4)(-4) = -64

Calculator

Order of Operation

1 Evaluate within grouping symbols [ ] ( )

innermost parenthesis first

2 Evaluate exponents

3 Multiply or Divide from left to right

4 Add or Subtract from left to right

Please Excuse My Dear Aunt Sally ndash PEMDAS

Remember its multiply or divide add or subtract

Parenthesis can be used to change the order of operations or to clarify the order

EXP 2 + 3 4 = 2 + (3 4) = 2 + 12 = 14

Learning the Order of Operations

Nested Parenthesis is one set inside another

Use the innermost parenthesis first

EXP EXP

Learning the Order of Operations

6[2 3(4 1)]

6[2 3(5)]

6[2 15]

6[17]

102

4[3(6 4) 6]

4[3(2) 6]

4[6 6]

4[1]

4

EXP EXP

Examples

23 2 4 8

3 2 16 8

3 32 8

35 8

27

25 4[ 3 (100 5 )]

5 4[ 3 (100 25)]

5 4[ 3 (4)]

5 4[1]

5 4

1

EXP EXP

Examples

2

2

(14 2) 5(3 2)

(7) 5(1)

7 5(1)

7 5

12

29 72 8 3 5

9 72 8 9 5

9 9 9 5

9 81 5

90 5

85

EXP EXP

Examples

25 18 3

25 18 3

25 6

19

2( 5) 18 3

25 18 3

25 6

31

EXP

Examples

4 3 2

7 5 9

4 3

7

1

2

5 9

3

4 2 = 105

7 15

4 15 60 2 7 14 and

7 15 105 15 7 105

60 14

105 105

46

105

LCD

Examples

Write the following statement as mathematical expressions using parentheses and brackets and then evaluate

Multiply 9 by 6 add 7 to this product Subtract 12 from the sum Divide this difference by 5

[[(9 6) + 7] ndash 12] divide 5

495

EXP

EXP

EXP

Evaluate Expressions Containing Variables

8 7 when 4

8(4) 732 725

x x

2

2 when 9

9 (9)(9) 81x x

2

2 when 9

9 (9)(9) 81x x

EXP

EXP

Evaluate Expressions Containing Variables

2

2 when 6

( 6) ( 6)( 6) 36y y

2

2 when 6

( 6) ( 6)( 6) 36y y

EXP

Evaluate Expressions Containing Variables

2

2

22 3 4 when

3

2 2 4 22 3 4 = 2 3 4

3 3 9 3

2 4 3 2 8 64 = 4 LCD = 9

1 9 1 3 9 3

8 18 10 4 10 364 = =

9 9 9 1 9 9

26 8 or 2

9 9

x x x

EXP

Evaluate Expressions Containing Variables

2

2

2( 7) 3 when 2 and 1

( 1) 2( 2 7) 3

1 2( 2 7) 3

1 2(5) 3

1 10 3

9 3

6

y x x y

HOMEWORK 19

Page 77 ndash 7818 21 29 35 43 57 61 75 79 83 87 95

Learning the Meaning of Exponents

Whenever we see a variable or number without an exponent we always assume that the exponent is 1

An exponent refers only to the number or variable that directly precedes it hellip unless parentheses are used to indicate otherwise

-x2 not the same as (-x)2

(-)(x)(x) (-x)(-x)

Learn the Meaning of Exponents

32 3 is called the base 2 is called the exponent2 factors of 3(3)(3) = 9

53

5 is called the base 3 is called the exponent3 factors of 5(5)(5)(5) = 125

17 pg 77) 52 ldquo5 squaredrdquo(5)(5) 5 is the base 2 is the exponent25 ldquo5 to the second powerrdquo

2 factors of 5

21 pg 77 73 ldquo7 cubedrdquo(7)(7)(7) ldquo7 to the third powerrdquo(49)(7) 3 factors of 7343 7 is the base 3 is the exponent

Exp b3 = bbb ldquob cubedrdquo

Exp x4 = xxxx ldquox to the fourthrdquo

Expamples

28) 53 19) 17

(5)(5)(5) (1)(1)(1)(1)(1)(1)(1)

(25)(5) 1

125

20) 41 37)

(4)

4

Examples

23 3 3 3 3 9

4 4 4 4 4 16

Write as an exponent

a) xyxx = x3y

b) xyzzy = xy2z2

c) 3aabb b = 3a2b3

d) 5xyyyy = 5xy3

e) (4)(4)rrs = 42r2s

f) (5)(5)(5)mmn = 53m2n

Exponential Notation

Exponents refer to the number or variable directly preceding it unless it is in

parenthesis

EXP -x2 only the x will be squared (-)(x)(x)

ldquonegative x squaredrdquo or ldquothe opposite of x squaredrdquo

EXP (-x)2 all will be squared (-x)(-x)

ldquonegative x quantity squaredrdquo

EXP -62 = (-)(6)(6) = -36

EXP (-6)2 = (-6)(-6)= 36

Difference between ndashx2 and (-x)2

30) (-7)2 even neg = pos result

(-7)(-7)

-49

Exp) (-4)4 even neg = pos result

(-4)(-4)(-4)(-4)

(16)(-4)(-4)

(-64)(-4)

256

Examples

exp) -102 exp) (-10)2

(-)(10)(10) (-10)(-10)

-100 100

exp) -43 exp) (-4)3 odd neg = neg result

(-)(4) (4)(4) (-4)(-4)(-4)

-64 (16)(-4)

-64

Examples

exp) (-3)4 exp) -(3)4

even neg = pos result

(-3)(-3)(-3)(-3) (-)(3)(3)(3)(3)

(9)(-3)(-3) (-3)(3)(3)(3)

(-27)(-3) (-9)(3)(3)

81 (-27)(3)

-81

Examples

EXP (-5)2 = (-5)(-5) = 25

EXP -(5)2 = -(5)(5) = -25

EXP -23 = -(2)(2)(2) = -8

EXP (-2)3 = (-2)(-2)(-2) = -8

EXP -24 = -(2)(2)(2)(2) = -16

EXP (-2)4 = (-2)(-2)(-2)(-2) = 16

EXP (-7)2 = (-7)(-7) = 49

EXP (-3)3 = (-3)(-3)(-3) = -27

Difference between ndashx2 and (-x)2

Help using your calculator is on page 70

EXP -102 = -(10)(10) = -100

EXP (-10)2 = (-10)(-10) = 100

EXP -43 = -(4)(4)(4) = -64

EXP (-4)3 = (-4)(-4)(-4) = -64

Calculator

Order of Operation

1 Evaluate within grouping symbols [ ] ( )

innermost parenthesis first

2 Evaluate exponents

3 Multiply or Divide from left to right

4 Add or Subtract from left to right

Please Excuse My Dear Aunt Sally ndash PEMDAS

Remember its multiply or divide add or subtract

Parenthesis can be used to change the order of operations or to clarify the order

EXP 2 + 3 4 = 2 + (3 4) = 2 + 12 = 14

Learning the Order of Operations

Nested Parenthesis is one set inside another

Use the innermost parenthesis first

EXP EXP

Learning the Order of Operations

6[2 3(4 1)]

6[2 3(5)]

6[2 15]

6[17]

102

4[3(6 4) 6]

4[3(2) 6]

4[6 6]

4[1]

4

EXP EXP

Examples

23 2 4 8

3 2 16 8

3 32 8

35 8

27

25 4[ 3 (100 5 )]

5 4[ 3 (100 25)]

5 4[ 3 (4)]

5 4[1]

5 4

1

EXP EXP

Examples

2

2

(14 2) 5(3 2)

(7) 5(1)

7 5(1)

7 5

12

29 72 8 3 5

9 72 8 9 5

9 9 9 5

9 81 5

90 5

85

EXP EXP

Examples

25 18 3

25 18 3

25 6

19

2( 5) 18 3

25 18 3

25 6

31

EXP

Examples

4 3 2

7 5 9

4 3

7

1

2

5 9

3

4 2 = 105

7 15

4 15 60 2 7 14 and

7 15 105 15 7 105

60 14

105 105

46

105

LCD

Examples

Write the following statement as mathematical expressions using parentheses and brackets and then evaluate

Multiply 9 by 6 add 7 to this product Subtract 12 from the sum Divide this difference by 5

[[(9 6) + 7] ndash 12] divide 5

495

EXP

EXP

EXP

Evaluate Expressions Containing Variables

8 7 when 4

8(4) 732 725

x x

2

2 when 9

9 (9)(9) 81x x

2

2 when 9

9 (9)(9) 81x x

EXP

EXP

Evaluate Expressions Containing Variables

2

2 when 6

( 6) ( 6)( 6) 36y y

2

2 when 6

( 6) ( 6)( 6) 36y y

EXP

Evaluate Expressions Containing Variables

2

2

22 3 4 when

3

2 2 4 22 3 4 = 2 3 4

3 3 9 3

2 4 3 2 8 64 = 4 LCD = 9

1 9 1 3 9 3

8 18 10 4 10 364 = =

9 9 9 1 9 9

26 8 or 2

9 9

x x x

EXP

Evaluate Expressions Containing Variables

2

2

2( 7) 3 when 2 and 1

( 1) 2( 2 7) 3

1 2( 2 7) 3

1 2(5) 3

1 10 3

9 3

6

y x x y

HOMEWORK 19

Page 77 ndash 7818 21 29 35 43 57 61 75 79 83 87 95

Learn the Meaning of Exponents

32 3 is called the base 2 is called the exponent2 factors of 3(3)(3) = 9

53

5 is called the base 3 is called the exponent3 factors of 5(5)(5)(5) = 125

17 pg 77) 52 ldquo5 squaredrdquo(5)(5) 5 is the base 2 is the exponent25 ldquo5 to the second powerrdquo

2 factors of 5

21 pg 77 73 ldquo7 cubedrdquo(7)(7)(7) ldquo7 to the third powerrdquo(49)(7) 3 factors of 7343 7 is the base 3 is the exponent

Exp b3 = bbb ldquob cubedrdquo

Exp x4 = xxxx ldquox to the fourthrdquo

Expamples

28) 53 19) 17

(5)(5)(5) (1)(1)(1)(1)(1)(1)(1)

(25)(5) 1

125

20) 41 37)

(4)

4

Examples

23 3 3 3 3 9

4 4 4 4 4 16

Write as an exponent

a) xyxx = x3y

b) xyzzy = xy2z2

c) 3aabb b = 3a2b3

d) 5xyyyy = 5xy3

e) (4)(4)rrs = 42r2s

f) (5)(5)(5)mmn = 53m2n

Exponential Notation

Exponents refer to the number or variable directly preceding it unless it is in

parenthesis

EXP -x2 only the x will be squared (-)(x)(x)

ldquonegative x squaredrdquo or ldquothe opposite of x squaredrdquo

EXP (-x)2 all will be squared (-x)(-x)

ldquonegative x quantity squaredrdquo

EXP -62 = (-)(6)(6) = -36

EXP (-6)2 = (-6)(-6)= 36

Difference between ndashx2 and (-x)2

30) (-7)2 even neg = pos result

(-7)(-7)

-49

Exp) (-4)4 even neg = pos result

(-4)(-4)(-4)(-4)

(16)(-4)(-4)

(-64)(-4)

256

Examples

exp) -102 exp) (-10)2

(-)(10)(10) (-10)(-10)

-100 100

exp) -43 exp) (-4)3 odd neg = neg result

(-)(4) (4)(4) (-4)(-4)(-4)

-64 (16)(-4)

-64

Examples

exp) (-3)4 exp) -(3)4

even neg = pos result

(-3)(-3)(-3)(-3) (-)(3)(3)(3)(3)

(9)(-3)(-3) (-3)(3)(3)(3)

(-27)(-3) (-9)(3)(3)

81 (-27)(3)

-81

Examples

EXP (-5)2 = (-5)(-5) = 25

EXP -(5)2 = -(5)(5) = -25

EXP -23 = -(2)(2)(2) = -8

EXP (-2)3 = (-2)(-2)(-2) = -8

EXP -24 = -(2)(2)(2)(2) = -16

EXP (-2)4 = (-2)(-2)(-2)(-2) = 16

EXP (-7)2 = (-7)(-7) = 49

EXP (-3)3 = (-3)(-3)(-3) = -27

Difference between ndashx2 and (-x)2

Help using your calculator is on page 70

EXP -102 = -(10)(10) = -100

EXP (-10)2 = (-10)(-10) = 100

EXP -43 = -(4)(4)(4) = -64

EXP (-4)3 = (-4)(-4)(-4) = -64

Calculator

Order of Operation

1 Evaluate within grouping symbols [ ] ( )

innermost parenthesis first

2 Evaluate exponents

3 Multiply or Divide from left to right

4 Add or Subtract from left to right

Please Excuse My Dear Aunt Sally ndash PEMDAS

Remember its multiply or divide add or subtract

Parenthesis can be used to change the order of operations or to clarify the order

EXP 2 + 3 4 = 2 + (3 4) = 2 + 12 = 14

Learning the Order of Operations

Nested Parenthesis is one set inside another

Use the innermost parenthesis first

EXP EXP

Learning the Order of Operations

6[2 3(4 1)]

6[2 3(5)]

6[2 15]

6[17]

102

4[3(6 4) 6]

4[3(2) 6]

4[6 6]

4[1]

4

EXP EXP

Examples

23 2 4 8

3 2 16 8

3 32 8

35 8

27

25 4[ 3 (100 5 )]

5 4[ 3 (100 25)]

5 4[ 3 (4)]

5 4[1]

5 4

1

EXP EXP

Examples

2

2

(14 2) 5(3 2)

(7) 5(1)

7 5(1)

7 5

12

29 72 8 3 5

9 72 8 9 5

9 9 9 5

9 81 5

90 5

85

EXP EXP

Examples

25 18 3

25 18 3

25 6

19

2( 5) 18 3

25 18 3

25 6

31

EXP

Examples

4 3 2

7 5 9

4 3

7

1

2

5 9

3

4 2 = 105

7 15

4 15 60 2 7 14 and

7 15 105 15 7 105

60 14

105 105

46

105

LCD

Examples

Write the following statement as mathematical expressions using parentheses and brackets and then evaluate

Multiply 9 by 6 add 7 to this product Subtract 12 from the sum Divide this difference by 5

[[(9 6) + 7] ndash 12] divide 5

495

EXP

EXP

EXP

Evaluate Expressions Containing Variables

8 7 when 4

8(4) 732 725

x x

2

2 when 9

9 (9)(9) 81x x

2

2 when 9

9 (9)(9) 81x x

EXP

EXP

Evaluate Expressions Containing Variables

2

2 when 6

( 6) ( 6)( 6) 36y y

2

2 when 6

( 6) ( 6)( 6) 36y y

EXP

Evaluate Expressions Containing Variables

2

2

22 3 4 when

3

2 2 4 22 3 4 = 2 3 4

3 3 9 3

2 4 3 2 8 64 = 4 LCD = 9

1 9 1 3 9 3

8 18 10 4 10 364 = =

9 9 9 1 9 9

26 8 or 2

9 9

x x x

EXP

Evaluate Expressions Containing Variables

2

2

2( 7) 3 when 2 and 1

( 1) 2( 2 7) 3

1 2( 2 7) 3

1 2(5) 3

1 10 3

9 3

6

y x x y

HOMEWORK 19

Page 77 ndash 7818 21 29 35 43 57 61 75 79 83 87 95

17 pg 77) 52 ldquo5 squaredrdquo(5)(5) 5 is the base 2 is the exponent25 ldquo5 to the second powerrdquo

2 factors of 5

21 pg 77 73 ldquo7 cubedrdquo(7)(7)(7) ldquo7 to the third powerrdquo(49)(7) 3 factors of 7343 7 is the base 3 is the exponent

Exp b3 = bbb ldquob cubedrdquo

Exp x4 = xxxx ldquox to the fourthrdquo

Expamples

28) 53 19) 17

(5)(5)(5) (1)(1)(1)(1)(1)(1)(1)

(25)(5) 1

125

20) 41 37)

(4)

4

Examples

23 3 3 3 3 9

4 4 4 4 4 16

Write as an exponent

a) xyxx = x3y

b) xyzzy = xy2z2

c) 3aabb b = 3a2b3

d) 5xyyyy = 5xy3

e) (4)(4)rrs = 42r2s

f) (5)(5)(5)mmn = 53m2n

Exponential Notation

Exponents refer to the number or variable directly preceding it unless it is in

parenthesis

EXP -x2 only the x will be squared (-)(x)(x)

ldquonegative x squaredrdquo or ldquothe opposite of x squaredrdquo

EXP (-x)2 all will be squared (-x)(-x)

ldquonegative x quantity squaredrdquo

EXP -62 = (-)(6)(6) = -36

EXP (-6)2 = (-6)(-6)= 36

Difference between ndashx2 and (-x)2

30) (-7)2 even neg = pos result

(-7)(-7)

-49

Exp) (-4)4 even neg = pos result

(-4)(-4)(-4)(-4)

(16)(-4)(-4)

(-64)(-4)

256

Examples

exp) -102 exp) (-10)2

(-)(10)(10) (-10)(-10)

-100 100

exp) -43 exp) (-4)3 odd neg = neg result

(-)(4) (4)(4) (-4)(-4)(-4)

-64 (16)(-4)

-64

Examples

exp) (-3)4 exp) -(3)4

even neg = pos result

(-3)(-3)(-3)(-3) (-)(3)(3)(3)(3)

(9)(-3)(-3) (-3)(3)(3)(3)

(-27)(-3) (-9)(3)(3)

81 (-27)(3)

-81

Examples

EXP (-5)2 = (-5)(-5) = 25

EXP -(5)2 = -(5)(5) = -25

EXP -23 = -(2)(2)(2) = -8

EXP (-2)3 = (-2)(-2)(-2) = -8

EXP -24 = -(2)(2)(2)(2) = -16

EXP (-2)4 = (-2)(-2)(-2)(-2) = 16

EXP (-7)2 = (-7)(-7) = 49

EXP (-3)3 = (-3)(-3)(-3) = -27

Difference between ndashx2 and (-x)2

Help using your calculator is on page 70

EXP -102 = -(10)(10) = -100

EXP (-10)2 = (-10)(-10) = 100

EXP -43 = -(4)(4)(4) = -64

EXP (-4)3 = (-4)(-4)(-4) = -64

Calculator

Order of Operation

1 Evaluate within grouping symbols [ ] ( )

innermost parenthesis first

2 Evaluate exponents

3 Multiply or Divide from left to right

4 Add or Subtract from left to right

Please Excuse My Dear Aunt Sally ndash PEMDAS

Remember its multiply or divide add or subtract

Parenthesis can be used to change the order of operations or to clarify the order

EXP 2 + 3 4 = 2 + (3 4) = 2 + 12 = 14

Learning the Order of Operations

Nested Parenthesis is one set inside another

Use the innermost parenthesis first

EXP EXP

Learning the Order of Operations

6[2 3(4 1)]

6[2 3(5)]

6[2 15]

6[17]

102

4[3(6 4) 6]

4[3(2) 6]

4[6 6]

4[1]

4

EXP EXP

Examples

23 2 4 8

3 2 16 8

3 32 8

35 8

27

25 4[ 3 (100 5 )]

5 4[ 3 (100 25)]

5 4[ 3 (4)]

5 4[1]

5 4

1

EXP EXP

Examples

2

2

(14 2) 5(3 2)

(7) 5(1)

7 5(1)

7 5

12

29 72 8 3 5

9 72 8 9 5

9 9 9 5

9 81 5

90 5

85

EXP EXP

Examples

25 18 3

25 18 3

25 6

19

2( 5) 18 3

25 18 3

25 6

31

EXP

Examples

4 3 2

7 5 9

4 3

7

1

2

5 9

3

4 2 = 105

7 15

4 15 60 2 7 14 and

7 15 105 15 7 105

60 14

105 105

46

105

LCD

Examples

Write the following statement as mathematical expressions using parentheses and brackets and then evaluate

Multiply 9 by 6 add 7 to this product Subtract 12 from the sum Divide this difference by 5

[[(9 6) + 7] ndash 12] divide 5

495

EXP

EXP

EXP

Evaluate Expressions Containing Variables

8 7 when 4

8(4) 732 725

x x

2

2 when 9

9 (9)(9) 81x x

2

2 when 9

9 (9)(9) 81x x

EXP

EXP

Evaluate Expressions Containing Variables

2

2 when 6

( 6) ( 6)( 6) 36y y

2

2 when 6

( 6) ( 6)( 6) 36y y

EXP

Evaluate Expressions Containing Variables

2

2

22 3 4 when

3

2 2 4 22 3 4 = 2 3 4

3 3 9 3

2 4 3 2 8 64 = 4 LCD = 9

1 9 1 3 9 3

8 18 10 4 10 364 = =

9 9 9 1 9 9

26 8 or 2

9 9

x x x

EXP

Evaluate Expressions Containing Variables

2

2

2( 7) 3 when 2 and 1

( 1) 2( 2 7) 3

1 2( 2 7) 3

1 2(5) 3

1 10 3

9 3

6

y x x y

HOMEWORK 19

Page 77 ndash 7818 21 29 35 43 57 61 75 79 83 87 95

28) 53 19) 17

(5)(5)(5) (1)(1)(1)(1)(1)(1)(1)

(25)(5) 1

125

20) 41 37)

(4)

4

Examples

23 3 3 3 3 9

4 4 4 4 4 16

Write as an exponent

a) xyxx = x3y

b) xyzzy = xy2z2

c) 3aabb b = 3a2b3

d) 5xyyyy = 5xy3

e) (4)(4)rrs = 42r2s

f) (5)(5)(5)mmn = 53m2n

Exponential Notation

Exponents refer to the number or variable directly preceding it unless it is in

parenthesis

EXP -x2 only the x will be squared (-)(x)(x)

ldquonegative x squaredrdquo or ldquothe opposite of x squaredrdquo

EXP (-x)2 all will be squared (-x)(-x)

ldquonegative x quantity squaredrdquo

EXP -62 = (-)(6)(6) = -36

EXP (-6)2 = (-6)(-6)= 36

Difference between ndashx2 and (-x)2

30) (-7)2 even neg = pos result

(-7)(-7)

-49

Exp) (-4)4 even neg = pos result

(-4)(-4)(-4)(-4)

(16)(-4)(-4)

(-64)(-4)

256

Examples

exp) -102 exp) (-10)2

(-)(10)(10) (-10)(-10)

-100 100

exp) -43 exp) (-4)3 odd neg = neg result

(-)(4) (4)(4) (-4)(-4)(-4)

-64 (16)(-4)

-64

Examples

exp) (-3)4 exp) -(3)4

even neg = pos result

(-3)(-3)(-3)(-3) (-)(3)(3)(3)(3)

(9)(-3)(-3) (-3)(3)(3)(3)

(-27)(-3) (-9)(3)(3)

81 (-27)(3)

-81

Examples

EXP (-5)2 = (-5)(-5) = 25

EXP -(5)2 = -(5)(5) = -25

EXP -23 = -(2)(2)(2) = -8

EXP (-2)3 = (-2)(-2)(-2) = -8

EXP -24 = -(2)(2)(2)(2) = -16

EXP (-2)4 = (-2)(-2)(-2)(-2) = 16

EXP (-7)2 = (-7)(-7) = 49

EXP (-3)3 = (-3)(-3)(-3) = -27

Difference between ndashx2 and (-x)2

Help using your calculator is on page 70

EXP -102 = -(10)(10) = -100

EXP (-10)2 = (-10)(-10) = 100

EXP -43 = -(4)(4)(4) = -64

EXP (-4)3 = (-4)(-4)(-4) = -64

Calculator

Order of Operation

1 Evaluate within grouping symbols [ ] ( )

innermost parenthesis first

2 Evaluate exponents

3 Multiply or Divide from left to right

4 Add or Subtract from left to right

Please Excuse My Dear Aunt Sally ndash PEMDAS

Remember its multiply or divide add or subtract

Parenthesis can be used to change the order of operations or to clarify the order

EXP 2 + 3 4 = 2 + (3 4) = 2 + 12 = 14

Learning the Order of Operations

Nested Parenthesis is one set inside another

Use the innermost parenthesis first

EXP EXP

Learning the Order of Operations

6[2 3(4 1)]

6[2 3(5)]

6[2 15]

6[17]

102

4[3(6 4) 6]

4[3(2) 6]

4[6 6]

4[1]

4

EXP EXP

Examples

23 2 4 8

3 2 16 8

3 32 8

35 8

27

25 4[ 3 (100 5 )]

5 4[ 3 (100 25)]

5 4[ 3 (4)]

5 4[1]

5 4

1

EXP EXP

Examples

2

2

(14 2) 5(3 2)

(7) 5(1)

7 5(1)

7 5

12

29 72 8 3 5

9 72 8 9 5

9 9 9 5

9 81 5

90 5

85

EXP EXP

Examples

25 18 3

25 18 3

25 6

19

2( 5) 18 3

25 18 3

25 6

31

EXP

Examples

4 3 2

7 5 9

4 3

7

1

2

5 9

3

4 2 = 105

7 15

4 15 60 2 7 14 and

7 15 105 15 7 105

60 14

105 105

46

105

LCD

Examples

Write the following statement as mathematical expressions using parentheses and brackets and then evaluate

Multiply 9 by 6 add 7 to this product Subtract 12 from the sum Divide this difference by 5

[[(9 6) + 7] ndash 12] divide 5

495

EXP

EXP

EXP

Evaluate Expressions Containing Variables

8 7 when 4

8(4) 732 725

x x

2

2 when 9

9 (9)(9) 81x x

2

2 when 9

9 (9)(9) 81x x

EXP

EXP

Evaluate Expressions Containing Variables

2

2 when 6

( 6) ( 6)( 6) 36y y

2

2 when 6

( 6) ( 6)( 6) 36y y

EXP

Evaluate Expressions Containing Variables

2

2

22 3 4 when

3

2 2 4 22 3 4 = 2 3 4

3 3 9 3

2 4 3 2 8 64 = 4 LCD = 9

1 9 1 3 9 3

8 18 10 4 10 364 = =

9 9 9 1 9 9

26 8 or 2

9 9

x x x

EXP

Evaluate Expressions Containing Variables

2

2

2( 7) 3 when 2 and 1

( 1) 2( 2 7) 3

1 2( 2 7) 3

1 2(5) 3

1 10 3

9 3

6

y x x y

HOMEWORK 19

Page 77 ndash 7818 21 29 35 43 57 61 75 79 83 87 95

Write as an exponent

a) xyxx = x3y

b) xyzzy = xy2z2

c) 3aabb b = 3a2b3

d) 5xyyyy = 5xy3

e) (4)(4)rrs = 42r2s

f) (5)(5)(5)mmn = 53m2n

Exponential Notation

Exponents refer to the number or variable directly preceding it unless it is in

parenthesis

EXP -x2 only the x will be squared (-)(x)(x)

ldquonegative x squaredrdquo or ldquothe opposite of x squaredrdquo

EXP (-x)2 all will be squared (-x)(-x)

ldquonegative x quantity squaredrdquo

EXP -62 = (-)(6)(6) = -36

EXP (-6)2 = (-6)(-6)= 36

Difference between ndashx2 and (-x)2

30) (-7)2 even neg = pos result

(-7)(-7)

-49

Exp) (-4)4 even neg = pos result

(-4)(-4)(-4)(-4)

(16)(-4)(-4)

(-64)(-4)

256

Examples

exp) -102 exp) (-10)2

(-)(10)(10) (-10)(-10)

-100 100

exp) -43 exp) (-4)3 odd neg = neg result

(-)(4) (4)(4) (-4)(-4)(-4)

-64 (16)(-4)

-64

Examples

exp) (-3)4 exp) -(3)4

even neg = pos result

(-3)(-3)(-3)(-3) (-)(3)(3)(3)(3)

(9)(-3)(-3) (-3)(3)(3)(3)

(-27)(-3) (-9)(3)(3)

81 (-27)(3)

-81

Examples

EXP (-5)2 = (-5)(-5) = 25

EXP -(5)2 = -(5)(5) = -25

EXP -23 = -(2)(2)(2) = -8

EXP (-2)3 = (-2)(-2)(-2) = -8

EXP -24 = -(2)(2)(2)(2) = -16

EXP (-2)4 = (-2)(-2)(-2)(-2) = 16

EXP (-7)2 = (-7)(-7) = 49

EXP (-3)3 = (-3)(-3)(-3) = -27

Difference between ndashx2 and (-x)2

Help using your calculator is on page 70

EXP -102 = -(10)(10) = -100

EXP (-10)2 = (-10)(-10) = 100

EXP -43 = -(4)(4)(4) = -64

EXP (-4)3 = (-4)(-4)(-4) = -64

Calculator

Order of Operation

1 Evaluate within grouping symbols [ ] ( )

innermost parenthesis first

2 Evaluate exponents

3 Multiply or Divide from left to right

4 Add or Subtract from left to right

Please Excuse My Dear Aunt Sally ndash PEMDAS

Remember its multiply or divide add or subtract

Parenthesis can be used to change the order of operations or to clarify the order

EXP 2 + 3 4 = 2 + (3 4) = 2 + 12 = 14

Learning the Order of Operations

Nested Parenthesis is one set inside another

Use the innermost parenthesis first

EXP EXP

Learning the Order of Operations

6[2 3(4 1)]

6[2 3(5)]

6[2 15]

6[17]

102

4[3(6 4) 6]

4[3(2) 6]

4[6 6]

4[1]

4

EXP EXP

Examples

23 2 4 8

3 2 16 8

3 32 8

35 8

27

25 4[ 3 (100 5 )]

5 4[ 3 (100 25)]

5 4[ 3 (4)]

5 4[1]

5 4

1

EXP EXP

Examples

2

2

(14 2) 5(3 2)

(7) 5(1)

7 5(1)

7 5

12

29 72 8 3 5

9 72 8 9 5

9 9 9 5

9 81 5

90 5

85

EXP EXP

Examples

25 18 3

25 18 3

25 6

19

2( 5) 18 3

25 18 3

25 6

31

EXP

Examples

4 3 2

7 5 9

4 3

7

1

2

5 9

3

4 2 = 105

7 15

4 15 60 2 7 14 and

7 15 105 15 7 105

60 14

105 105

46

105

LCD

Examples

Write the following statement as mathematical expressions using parentheses and brackets and then evaluate

Multiply 9 by 6 add 7 to this product Subtract 12 from the sum Divide this difference by 5

[[(9 6) + 7] ndash 12] divide 5

495

EXP

EXP

EXP

Evaluate Expressions Containing Variables

8 7 when 4

8(4) 732 725

x x

2

2 when 9

9 (9)(9) 81x x

2

2 when 9

9 (9)(9) 81x x

EXP

EXP

Evaluate Expressions Containing Variables

2

2 when 6

( 6) ( 6)( 6) 36y y

2

2 when 6

( 6) ( 6)( 6) 36y y

EXP

Evaluate Expressions Containing Variables

2

2

22 3 4 when

3

2 2 4 22 3 4 = 2 3 4

3 3 9 3

2 4 3 2 8 64 = 4 LCD = 9

1 9 1 3 9 3

8 18 10 4 10 364 = =

9 9 9 1 9 9

26 8 or 2

9 9

x x x

EXP

Evaluate Expressions Containing Variables

2

2

2( 7) 3 when 2 and 1

( 1) 2( 2 7) 3

1 2( 2 7) 3

1 2(5) 3

1 10 3

9 3

6

y x x y

HOMEWORK 19

Page 77 ndash 7818 21 29 35 43 57 61 75 79 83 87 95

Exponents refer to the number or variable directly preceding it unless it is in

parenthesis

EXP -x2 only the x will be squared (-)(x)(x)

ldquonegative x squaredrdquo or ldquothe opposite of x squaredrdquo

EXP (-x)2 all will be squared (-x)(-x)

ldquonegative x quantity squaredrdquo

EXP -62 = (-)(6)(6) = -36

EXP (-6)2 = (-6)(-6)= 36

Difference between ndashx2 and (-x)2

30) (-7)2 even neg = pos result

(-7)(-7)

-49

Exp) (-4)4 even neg = pos result

(-4)(-4)(-4)(-4)

(16)(-4)(-4)

(-64)(-4)

256

Examples

exp) -102 exp) (-10)2

(-)(10)(10) (-10)(-10)

-100 100

exp) -43 exp) (-4)3 odd neg = neg result

(-)(4) (4)(4) (-4)(-4)(-4)

-64 (16)(-4)

-64

Examples

exp) (-3)4 exp) -(3)4

even neg = pos result

(-3)(-3)(-3)(-3) (-)(3)(3)(3)(3)

(9)(-3)(-3) (-3)(3)(3)(3)

(-27)(-3) (-9)(3)(3)

81 (-27)(3)

-81

Examples

EXP (-5)2 = (-5)(-5) = 25

EXP -(5)2 = -(5)(5) = -25

EXP -23 = -(2)(2)(2) = -8

EXP (-2)3 = (-2)(-2)(-2) = -8

EXP -24 = -(2)(2)(2)(2) = -16

EXP (-2)4 = (-2)(-2)(-2)(-2) = 16

EXP (-7)2 = (-7)(-7) = 49

EXP (-3)3 = (-3)(-3)(-3) = -27

Difference between ndashx2 and (-x)2

Help using your calculator is on page 70

EXP -102 = -(10)(10) = -100

EXP (-10)2 = (-10)(-10) = 100

EXP -43 = -(4)(4)(4) = -64

EXP (-4)3 = (-4)(-4)(-4) = -64

Calculator

Order of Operation

1 Evaluate within grouping symbols [ ] ( )

innermost parenthesis first

2 Evaluate exponents

3 Multiply or Divide from left to right

4 Add or Subtract from left to right

Please Excuse My Dear Aunt Sally ndash PEMDAS

Remember its multiply or divide add or subtract

Parenthesis can be used to change the order of operations or to clarify the order

EXP 2 + 3 4 = 2 + (3 4) = 2 + 12 = 14

Learning the Order of Operations

Nested Parenthesis is one set inside another

Use the innermost parenthesis first

EXP EXP

Learning the Order of Operations

6[2 3(4 1)]

6[2 3(5)]

6[2 15]

6[17]

102

4[3(6 4) 6]

4[3(2) 6]

4[6 6]

4[1]

4

EXP EXP

Examples

23 2 4 8

3 2 16 8

3 32 8

35 8

27

25 4[ 3 (100 5 )]

5 4[ 3 (100 25)]

5 4[ 3 (4)]

5 4[1]

5 4

1

EXP EXP

Examples

2

2

(14 2) 5(3 2)

(7) 5(1)

7 5(1)

7 5

12

29 72 8 3 5

9 72 8 9 5

9 9 9 5

9 81 5

90 5

85

EXP EXP

Examples

25 18 3

25 18 3

25 6

19

2( 5) 18 3

25 18 3

25 6

31

EXP

Examples

4 3 2

7 5 9

4 3

7

1

2

5 9

3

4 2 = 105

7 15

4 15 60 2 7 14 and

7 15 105 15 7 105

60 14

105 105

46

105

LCD

Examples

Write the following statement as mathematical expressions using parentheses and brackets and then evaluate

Multiply 9 by 6 add 7 to this product Subtract 12 from the sum Divide this difference by 5

[[(9 6) + 7] ndash 12] divide 5

495

EXP

EXP

EXP

Evaluate Expressions Containing Variables

8 7 when 4

8(4) 732 725

x x

2

2 when 9

9 (9)(9) 81x x

2

2 when 9

9 (9)(9) 81x x

EXP

EXP

Evaluate Expressions Containing Variables

2

2 when 6

( 6) ( 6)( 6) 36y y

2

2 when 6

( 6) ( 6)( 6) 36y y

EXP

Evaluate Expressions Containing Variables

2

2

22 3 4 when

3

2 2 4 22 3 4 = 2 3 4

3 3 9 3

2 4 3 2 8 64 = 4 LCD = 9

1 9 1 3 9 3

8 18 10 4 10 364 = =

9 9 9 1 9 9

26 8 or 2

9 9

x x x

EXP

Evaluate Expressions Containing Variables

2

2

2( 7) 3 when 2 and 1

( 1) 2( 2 7) 3

1 2( 2 7) 3

1 2(5) 3

1 10 3

9 3

6

y x x y

HOMEWORK 19

Page 77 ndash 7818 21 29 35 43 57 61 75 79 83 87 95

30) (-7)2 even neg = pos result

(-7)(-7)

-49

Exp) (-4)4 even neg = pos result

(-4)(-4)(-4)(-4)

(16)(-4)(-4)

(-64)(-4)

256

Examples

exp) -102 exp) (-10)2

(-)(10)(10) (-10)(-10)

-100 100

exp) -43 exp) (-4)3 odd neg = neg result

(-)(4) (4)(4) (-4)(-4)(-4)

-64 (16)(-4)

-64

Examples

exp) (-3)4 exp) -(3)4

even neg = pos result

(-3)(-3)(-3)(-3) (-)(3)(3)(3)(3)

(9)(-3)(-3) (-3)(3)(3)(3)

(-27)(-3) (-9)(3)(3)

81 (-27)(3)

-81

Examples

EXP (-5)2 = (-5)(-5) = 25

EXP -(5)2 = -(5)(5) = -25

EXP -23 = -(2)(2)(2) = -8

EXP (-2)3 = (-2)(-2)(-2) = -8

EXP -24 = -(2)(2)(2)(2) = -16

EXP (-2)4 = (-2)(-2)(-2)(-2) = 16

EXP (-7)2 = (-7)(-7) = 49

EXP (-3)3 = (-3)(-3)(-3) = -27

Difference between ndashx2 and (-x)2

Help using your calculator is on page 70

EXP -102 = -(10)(10) = -100

EXP (-10)2 = (-10)(-10) = 100

EXP -43 = -(4)(4)(4) = -64

EXP (-4)3 = (-4)(-4)(-4) = -64

Calculator

Order of Operation

1 Evaluate within grouping symbols [ ] ( )

innermost parenthesis first

2 Evaluate exponents

3 Multiply or Divide from left to right

4 Add or Subtract from left to right

Please Excuse My Dear Aunt Sally ndash PEMDAS

Remember its multiply or divide add or subtract

Parenthesis can be used to change the order of operations or to clarify the order

EXP 2 + 3 4 = 2 + (3 4) = 2 + 12 = 14

Learning the Order of Operations

Nested Parenthesis is one set inside another

Use the innermost parenthesis first

EXP EXP

Learning the Order of Operations

6[2 3(4 1)]

6[2 3(5)]

6[2 15]

6[17]

102

4[3(6 4) 6]

4[3(2) 6]

4[6 6]

4[1]

4

EXP EXP

Examples

23 2 4 8

3 2 16 8

3 32 8

35 8

27

25 4[ 3 (100 5 )]

5 4[ 3 (100 25)]

5 4[ 3 (4)]

5 4[1]

5 4

1

EXP EXP

Examples

2

2

(14 2) 5(3 2)

(7) 5(1)

7 5(1)

7 5

12

29 72 8 3 5

9 72 8 9 5

9 9 9 5

9 81 5

90 5

85

EXP EXP

Examples

25 18 3

25 18 3

25 6

19

2( 5) 18 3

25 18 3

25 6

31

EXP

Examples

4 3 2

7 5 9

4 3

7

1

2

5 9

3

4 2 = 105

7 15

4 15 60 2 7 14 and

7 15 105 15 7 105

60 14

105 105

46

105

LCD

Examples

Write the following statement as mathematical expressions using parentheses and brackets and then evaluate

Multiply 9 by 6 add 7 to this product Subtract 12 from the sum Divide this difference by 5

[[(9 6) + 7] ndash 12] divide 5

495

EXP

EXP

EXP

Evaluate Expressions Containing Variables

8 7 when 4

8(4) 732 725

x x

2

2 when 9

9 (9)(9) 81x x

2

2 when 9

9 (9)(9) 81x x

EXP

EXP

Evaluate Expressions Containing Variables

2

2 when 6

( 6) ( 6)( 6) 36y y

2

2 when 6

( 6) ( 6)( 6) 36y y

EXP

Evaluate Expressions Containing Variables

2

2

22 3 4 when

3

2 2 4 22 3 4 = 2 3 4

3 3 9 3

2 4 3 2 8 64 = 4 LCD = 9

1 9 1 3 9 3

8 18 10 4 10 364 = =

9 9 9 1 9 9

26 8 or 2

9 9

x x x

EXP

Evaluate Expressions Containing Variables

2

2

2( 7) 3 when 2 and 1

( 1) 2( 2 7) 3

1 2( 2 7) 3

1 2(5) 3

1 10 3

9 3

6

y x x y

HOMEWORK 19

Page 77 ndash 7818 21 29 35 43 57 61 75 79 83 87 95

exp) -102 exp) (-10)2

(-)(10)(10) (-10)(-10)

-100 100

exp) -43 exp) (-4)3 odd neg = neg result

(-)(4) (4)(4) (-4)(-4)(-4)

-64 (16)(-4)

-64

Examples

exp) (-3)4 exp) -(3)4

even neg = pos result

(-3)(-3)(-3)(-3) (-)(3)(3)(3)(3)

(9)(-3)(-3) (-3)(3)(3)(3)

(-27)(-3) (-9)(3)(3)

81 (-27)(3)

-81

Examples

EXP (-5)2 = (-5)(-5) = 25

EXP -(5)2 = -(5)(5) = -25

EXP -23 = -(2)(2)(2) = -8

EXP (-2)3 = (-2)(-2)(-2) = -8

EXP -24 = -(2)(2)(2)(2) = -16

EXP (-2)4 = (-2)(-2)(-2)(-2) = 16

EXP (-7)2 = (-7)(-7) = 49

EXP (-3)3 = (-3)(-3)(-3) = -27

Difference between ndashx2 and (-x)2

Help using your calculator is on page 70

EXP -102 = -(10)(10) = -100

EXP (-10)2 = (-10)(-10) = 100

EXP -43 = -(4)(4)(4) = -64

EXP (-4)3 = (-4)(-4)(-4) = -64

Calculator

Order of Operation

1 Evaluate within grouping symbols [ ] ( )

innermost parenthesis first

2 Evaluate exponents

3 Multiply or Divide from left to right

4 Add or Subtract from left to right

Please Excuse My Dear Aunt Sally ndash PEMDAS

Remember its multiply or divide add or subtract

Parenthesis can be used to change the order of operations or to clarify the order

EXP 2 + 3 4 = 2 + (3 4) = 2 + 12 = 14

Learning the Order of Operations

Nested Parenthesis is one set inside another

Use the innermost parenthesis first

EXP EXP

Learning the Order of Operations

6[2 3(4 1)]

6[2 3(5)]

6[2 15]

6[17]

102

4[3(6 4) 6]

4[3(2) 6]

4[6 6]

4[1]

4

EXP EXP

Examples

23 2 4 8

3 2 16 8

3 32 8

35 8

27

25 4[ 3 (100 5 )]

5 4[ 3 (100 25)]

5 4[ 3 (4)]

5 4[1]

5 4

1

EXP EXP

Examples

2

2

(14 2) 5(3 2)

(7) 5(1)

7 5(1)

7 5

12

29 72 8 3 5

9 72 8 9 5

9 9 9 5

9 81 5

90 5

85

EXP EXP

Examples

25 18 3

25 18 3

25 6

19

2( 5) 18 3

25 18 3

25 6

31

EXP

Examples

4 3 2

7 5 9

4 3

7

1

2

5 9

3

4 2 = 105

7 15

4 15 60 2 7 14 and

7 15 105 15 7 105

60 14

105 105

46

105

LCD

Examples

Write the following statement as mathematical expressions using parentheses and brackets and then evaluate

Multiply 9 by 6 add 7 to this product Subtract 12 from the sum Divide this difference by 5

[[(9 6) + 7] ndash 12] divide 5

495

EXP

EXP

EXP

Evaluate Expressions Containing Variables

8 7 when 4

8(4) 732 725

x x

2

2 when 9

9 (9)(9) 81x x

2

2 when 9

9 (9)(9) 81x x

EXP

EXP

Evaluate Expressions Containing Variables

2

2 when 6

( 6) ( 6)( 6) 36y y

2

2 when 6

( 6) ( 6)( 6) 36y y

EXP

Evaluate Expressions Containing Variables

2

2

22 3 4 when

3

2 2 4 22 3 4 = 2 3 4

3 3 9 3

2 4 3 2 8 64 = 4 LCD = 9

1 9 1 3 9 3

8 18 10 4 10 364 = =

9 9 9 1 9 9

26 8 or 2

9 9

x x x

EXP

Evaluate Expressions Containing Variables

2

2

2( 7) 3 when 2 and 1

( 1) 2( 2 7) 3

1 2( 2 7) 3

1 2(5) 3

1 10 3

9 3

6

y x x y

HOMEWORK 19

Page 77 ndash 7818 21 29 35 43 57 61 75 79 83 87 95

exp) (-3)4 exp) -(3)4

even neg = pos result

(-3)(-3)(-3)(-3) (-)(3)(3)(3)(3)

(9)(-3)(-3) (-3)(3)(3)(3)

(-27)(-3) (-9)(3)(3)

81 (-27)(3)

-81

Examples

EXP (-5)2 = (-5)(-5) = 25

EXP -(5)2 = -(5)(5) = -25

EXP -23 = -(2)(2)(2) = -8

EXP (-2)3 = (-2)(-2)(-2) = -8

EXP -24 = -(2)(2)(2)(2) = -16

EXP (-2)4 = (-2)(-2)(-2)(-2) = 16

EXP (-7)2 = (-7)(-7) = 49

EXP (-3)3 = (-3)(-3)(-3) = -27

Difference between ndashx2 and (-x)2

Help using your calculator is on page 70

EXP -102 = -(10)(10) = -100

EXP (-10)2 = (-10)(-10) = 100

EXP -43 = -(4)(4)(4) = -64

EXP (-4)3 = (-4)(-4)(-4) = -64

Calculator

Order of Operation

1 Evaluate within grouping symbols [ ] ( )

innermost parenthesis first

2 Evaluate exponents

3 Multiply or Divide from left to right

4 Add or Subtract from left to right

Please Excuse My Dear Aunt Sally ndash PEMDAS

Remember its multiply or divide add or subtract

Parenthesis can be used to change the order of operations or to clarify the order

EXP 2 + 3 4 = 2 + (3 4) = 2 + 12 = 14

Learning the Order of Operations

Nested Parenthesis is one set inside another

Use the innermost parenthesis first

EXP EXP

Learning the Order of Operations

6[2 3(4 1)]

6[2 3(5)]

6[2 15]

6[17]

102

4[3(6 4) 6]

4[3(2) 6]

4[6 6]

4[1]

4

EXP EXP

Examples

23 2 4 8

3 2 16 8

3 32 8

35 8

27

25 4[ 3 (100 5 )]

5 4[ 3 (100 25)]

5 4[ 3 (4)]

5 4[1]

5 4

1

EXP EXP

Examples

2

2

(14 2) 5(3 2)

(7) 5(1)

7 5(1)

7 5

12

29 72 8 3 5

9 72 8 9 5

9 9 9 5

9 81 5

90 5

85

EXP EXP

Examples

25 18 3

25 18 3

25 6

19

2( 5) 18 3

25 18 3

25 6

31

EXP

Examples

4 3 2

7 5 9

4 3

7

1

2

5 9

3

4 2 = 105

7 15

4 15 60 2 7 14 and

7 15 105 15 7 105

60 14

105 105

46

105

LCD

Examples

Write the following statement as mathematical expressions using parentheses and brackets and then evaluate

Multiply 9 by 6 add 7 to this product Subtract 12 from the sum Divide this difference by 5

[[(9 6) + 7] ndash 12] divide 5

495

EXP

EXP

EXP

Evaluate Expressions Containing Variables

8 7 when 4

8(4) 732 725

x x

2

2 when 9

9 (9)(9) 81x x

2

2 when 9

9 (9)(9) 81x x

EXP

EXP

Evaluate Expressions Containing Variables

2

2 when 6

( 6) ( 6)( 6) 36y y

2

2 when 6

( 6) ( 6)( 6) 36y y

EXP

Evaluate Expressions Containing Variables

2

2

22 3 4 when

3

2 2 4 22 3 4 = 2 3 4

3 3 9 3

2 4 3 2 8 64 = 4 LCD = 9

1 9 1 3 9 3

8 18 10 4 10 364 = =

9 9 9 1 9 9

26 8 or 2

9 9

x x x

EXP

Evaluate Expressions Containing Variables

2

2

2( 7) 3 when 2 and 1

( 1) 2( 2 7) 3

1 2( 2 7) 3

1 2(5) 3

1 10 3

9 3

6

y x x y

HOMEWORK 19

Page 77 ndash 7818 21 29 35 43 57 61 75 79 83 87 95

EXP (-5)2 = (-5)(-5) = 25

EXP -(5)2 = -(5)(5) = -25

EXP -23 = -(2)(2)(2) = -8

EXP (-2)3 = (-2)(-2)(-2) = -8

EXP -24 = -(2)(2)(2)(2) = -16

EXP (-2)4 = (-2)(-2)(-2)(-2) = 16

EXP (-7)2 = (-7)(-7) = 49

EXP (-3)3 = (-3)(-3)(-3) = -27

Difference between ndashx2 and (-x)2

Help using your calculator is on page 70

EXP -102 = -(10)(10) = -100

EXP (-10)2 = (-10)(-10) = 100

EXP -43 = -(4)(4)(4) = -64

EXP (-4)3 = (-4)(-4)(-4) = -64

Calculator

Order of Operation

1 Evaluate within grouping symbols [ ] ( )

innermost parenthesis first

2 Evaluate exponents

3 Multiply or Divide from left to right

4 Add or Subtract from left to right

Please Excuse My Dear Aunt Sally ndash PEMDAS

Remember its multiply or divide add or subtract

Parenthesis can be used to change the order of operations or to clarify the order

EXP 2 + 3 4 = 2 + (3 4) = 2 + 12 = 14

Learning the Order of Operations

Nested Parenthesis is one set inside another

Use the innermost parenthesis first

EXP EXP

Learning the Order of Operations

6[2 3(4 1)]

6[2 3(5)]

6[2 15]

6[17]

102

4[3(6 4) 6]

4[3(2) 6]

4[6 6]

4[1]

4

EXP EXP

Examples

23 2 4 8

3 2 16 8

3 32 8

35 8

27

25 4[ 3 (100 5 )]

5 4[ 3 (100 25)]

5 4[ 3 (4)]

5 4[1]

5 4

1

EXP EXP

Examples

2

2

(14 2) 5(3 2)

(7) 5(1)

7 5(1)

7 5

12

29 72 8 3 5

9 72 8 9 5

9 9 9 5

9 81 5

90 5

85

EXP EXP

Examples

25 18 3

25 18 3

25 6

19

2( 5) 18 3

25 18 3

25 6

31

EXP

Examples

4 3 2

7 5 9

4 3

7

1

2

5 9

3

4 2 = 105

7 15

4 15 60 2 7 14 and

7 15 105 15 7 105

60 14

105 105

46

105

LCD

Examples

Write the following statement as mathematical expressions using parentheses and brackets and then evaluate

Multiply 9 by 6 add 7 to this product Subtract 12 from the sum Divide this difference by 5

[[(9 6) + 7] ndash 12] divide 5

495

EXP

EXP

EXP

Evaluate Expressions Containing Variables

8 7 when 4

8(4) 732 725

x x

2

2 when 9

9 (9)(9) 81x x

2

2 when 9

9 (9)(9) 81x x

EXP

EXP

Evaluate Expressions Containing Variables

2

2 when 6

( 6) ( 6)( 6) 36y y

2

2 when 6

( 6) ( 6)( 6) 36y y

EXP

Evaluate Expressions Containing Variables

2

2

22 3 4 when

3

2 2 4 22 3 4 = 2 3 4

3 3 9 3

2 4 3 2 8 64 = 4 LCD = 9

1 9 1 3 9 3

8 18 10 4 10 364 = =

9 9 9 1 9 9

26 8 or 2

9 9

x x x

EXP

Evaluate Expressions Containing Variables

2

2

2( 7) 3 when 2 and 1

( 1) 2( 2 7) 3

1 2( 2 7) 3

1 2(5) 3

1 10 3

9 3

6

y x x y

HOMEWORK 19

Page 77 ndash 7818 21 29 35 43 57 61 75 79 83 87 95

Help using your calculator is on page 70

EXP -102 = -(10)(10) = -100

EXP (-10)2 = (-10)(-10) = 100

EXP -43 = -(4)(4)(4) = -64

EXP (-4)3 = (-4)(-4)(-4) = -64

Calculator

Order of Operation

1 Evaluate within grouping symbols [ ] ( )

innermost parenthesis first

2 Evaluate exponents

3 Multiply or Divide from left to right

4 Add or Subtract from left to right

Please Excuse My Dear Aunt Sally ndash PEMDAS

Remember its multiply or divide add or subtract

Parenthesis can be used to change the order of operations or to clarify the order

EXP 2 + 3 4 = 2 + (3 4) = 2 + 12 = 14

Learning the Order of Operations

Nested Parenthesis is one set inside another

Use the innermost parenthesis first

EXP EXP

Learning the Order of Operations

6[2 3(4 1)]

6[2 3(5)]

6[2 15]

6[17]

102

4[3(6 4) 6]

4[3(2) 6]

4[6 6]

4[1]

4

EXP EXP

Examples

23 2 4 8

3 2 16 8

3 32 8

35 8

27

25 4[ 3 (100 5 )]

5 4[ 3 (100 25)]

5 4[ 3 (4)]

5 4[1]

5 4

1

EXP EXP

Examples

2

2

(14 2) 5(3 2)

(7) 5(1)

7 5(1)

7 5

12

29 72 8 3 5

9 72 8 9 5

9 9 9 5

9 81 5

90 5

85

EXP EXP

Examples

25 18 3

25 18 3

25 6

19

2( 5) 18 3

25 18 3

25 6

31

EXP

Examples

4 3 2

7 5 9

4 3

7

1

2

5 9

3

4 2 = 105

7 15

4 15 60 2 7 14 and

7 15 105 15 7 105

60 14

105 105

46

105

LCD

Examples

Write the following statement as mathematical expressions using parentheses and brackets and then evaluate

Multiply 9 by 6 add 7 to this product Subtract 12 from the sum Divide this difference by 5

[[(9 6) + 7] ndash 12] divide 5

495

EXP

EXP

EXP

Evaluate Expressions Containing Variables

8 7 when 4

8(4) 732 725

x x

2

2 when 9

9 (9)(9) 81x x

2

2 when 9

9 (9)(9) 81x x

EXP

EXP

Evaluate Expressions Containing Variables

2

2 when 6

( 6) ( 6)( 6) 36y y

2

2 when 6

( 6) ( 6)( 6) 36y y

EXP

Evaluate Expressions Containing Variables

2

2

22 3 4 when

3

2 2 4 22 3 4 = 2 3 4

3 3 9 3

2 4 3 2 8 64 = 4 LCD = 9

1 9 1 3 9 3

8 18 10 4 10 364 = =

9 9 9 1 9 9

26 8 or 2

9 9

x x x

EXP

Evaluate Expressions Containing Variables

2

2

2( 7) 3 when 2 and 1

( 1) 2( 2 7) 3

1 2( 2 7) 3

1 2(5) 3

1 10 3

9 3

6

y x x y

HOMEWORK 19

Page 77 ndash 7818 21 29 35 43 57 61 75 79 83 87 95

Order of Operation

1 Evaluate within grouping symbols [ ] ( )

innermost parenthesis first

2 Evaluate exponents

3 Multiply or Divide from left to right

4 Add or Subtract from left to right

Please Excuse My Dear Aunt Sally ndash PEMDAS

Remember its multiply or divide add or subtract

Parenthesis can be used to change the order of operations or to clarify the order

EXP 2 + 3 4 = 2 + (3 4) = 2 + 12 = 14

Learning the Order of Operations

Nested Parenthesis is one set inside another

Use the innermost parenthesis first

EXP EXP

Learning the Order of Operations

6[2 3(4 1)]

6[2 3(5)]

6[2 15]

6[17]

102

4[3(6 4) 6]

4[3(2) 6]

4[6 6]

4[1]

4

EXP EXP

Examples

23 2 4 8

3 2 16 8

3 32 8

35 8

27

25 4[ 3 (100 5 )]

5 4[ 3 (100 25)]

5 4[ 3 (4)]

5 4[1]

5 4

1

EXP EXP

Examples

2

2

(14 2) 5(3 2)

(7) 5(1)

7 5(1)

7 5

12

29 72 8 3 5

9 72 8 9 5

9 9 9 5

9 81 5

90 5

85

EXP EXP

Examples

25 18 3

25 18 3

25 6

19

2( 5) 18 3

25 18 3

25 6

31

EXP

Examples

4 3 2

7 5 9

4 3

7

1

2

5 9

3

4 2 = 105

7 15

4 15 60 2 7 14 and

7 15 105 15 7 105

60 14

105 105

46

105

LCD

Examples

Write the following statement as mathematical expressions using parentheses and brackets and then evaluate

Multiply 9 by 6 add 7 to this product Subtract 12 from the sum Divide this difference by 5

[[(9 6) + 7] ndash 12] divide 5

495

EXP

EXP

EXP

Evaluate Expressions Containing Variables

8 7 when 4

8(4) 732 725

x x

2

2 when 9

9 (9)(9) 81x x

2

2 when 9

9 (9)(9) 81x x

EXP

EXP

Evaluate Expressions Containing Variables

2

2 when 6

( 6) ( 6)( 6) 36y y

2

2 when 6

( 6) ( 6)( 6) 36y y

EXP

Evaluate Expressions Containing Variables

2

2

22 3 4 when

3

2 2 4 22 3 4 = 2 3 4

3 3 9 3

2 4 3 2 8 64 = 4 LCD = 9

1 9 1 3 9 3

8 18 10 4 10 364 = =

9 9 9 1 9 9

26 8 or 2

9 9

x x x

EXP

Evaluate Expressions Containing Variables

2

2

2( 7) 3 when 2 and 1

( 1) 2( 2 7) 3

1 2( 2 7) 3

1 2(5) 3

1 10 3

9 3

6

y x x y

HOMEWORK 19

Page 77 ndash 7818 21 29 35 43 57 61 75 79 83 87 95

Nested Parenthesis is one set inside another

Use the innermost parenthesis first

EXP EXP

Learning the Order of Operations

6[2 3(4 1)]

6[2 3(5)]

6[2 15]

6[17]

102

4[3(6 4) 6]

4[3(2) 6]

4[6 6]

4[1]

4

EXP EXP

Examples

23 2 4 8

3 2 16 8

3 32 8

35 8

27

25 4[ 3 (100 5 )]

5 4[ 3 (100 25)]

5 4[ 3 (4)]

5 4[1]

5 4

1

EXP EXP

Examples

2

2

(14 2) 5(3 2)

(7) 5(1)

7 5(1)

7 5

12

29 72 8 3 5

9 72 8 9 5

9 9 9 5

9 81 5

90 5

85

EXP EXP

Examples

25 18 3

25 18 3

25 6

19

2( 5) 18 3

25 18 3

25 6

31

EXP

Examples

4 3 2

7 5 9

4 3

7

1

2

5 9

3

4 2 = 105

7 15

4 15 60 2 7 14 and

7 15 105 15 7 105

60 14

105 105

46

105

LCD

Examples

Write the following statement as mathematical expressions using parentheses and brackets and then evaluate

Multiply 9 by 6 add 7 to this product Subtract 12 from the sum Divide this difference by 5

[[(9 6) + 7] ndash 12] divide 5

495

EXP

EXP

EXP

Evaluate Expressions Containing Variables

8 7 when 4

8(4) 732 725

x x

2

2 when 9

9 (9)(9) 81x x

2

2 when 9

9 (9)(9) 81x x

EXP

EXP

Evaluate Expressions Containing Variables

2

2 when 6

( 6) ( 6)( 6) 36y y

2

2 when 6

( 6) ( 6)( 6) 36y y

EXP

Evaluate Expressions Containing Variables

2

2

22 3 4 when

3

2 2 4 22 3 4 = 2 3 4

3 3 9 3

2 4 3 2 8 64 = 4 LCD = 9

1 9 1 3 9 3

8 18 10 4 10 364 = =

9 9 9 1 9 9

26 8 or 2

9 9

x x x

EXP

Evaluate Expressions Containing Variables

2

2

2( 7) 3 when 2 and 1

( 1) 2( 2 7) 3

1 2( 2 7) 3

1 2(5) 3

1 10 3

9 3

6

y x x y

HOMEWORK 19

Page 77 ndash 7818 21 29 35 43 57 61 75 79 83 87 95

EXP EXP

Examples

23 2 4 8

3 2 16 8

3 32 8

35 8

27

25 4[ 3 (100 5 )]

5 4[ 3 (100 25)]

5 4[ 3 (4)]

5 4[1]

5 4

1

EXP EXP

Examples

2

2

(14 2) 5(3 2)

(7) 5(1)

7 5(1)

7 5

12

29 72 8 3 5

9 72 8 9 5

9 9 9 5

9 81 5

90 5

85

EXP EXP

Examples

25 18 3

25 18 3

25 6

19

2( 5) 18 3

25 18 3

25 6

31

EXP

Examples

4 3 2

7 5 9

4 3

7

1

2

5 9

3

4 2 = 105

7 15

4 15 60 2 7 14 and

7 15 105 15 7 105

60 14

105 105

46

105

LCD

Examples

Write the following statement as mathematical expressions using parentheses and brackets and then evaluate

Multiply 9 by 6 add 7 to this product Subtract 12 from the sum Divide this difference by 5

[[(9 6) + 7] ndash 12] divide 5

495

EXP

EXP

EXP

Evaluate Expressions Containing Variables

8 7 when 4

8(4) 732 725

x x

2

2 when 9

9 (9)(9) 81x x

2

2 when 9

9 (9)(9) 81x x

EXP

EXP

Evaluate Expressions Containing Variables

2

2 when 6

( 6) ( 6)( 6) 36y y

2

2 when 6

( 6) ( 6)( 6) 36y y

EXP

Evaluate Expressions Containing Variables

2

2

22 3 4 when

3

2 2 4 22 3 4 = 2 3 4

3 3 9 3

2 4 3 2 8 64 = 4 LCD = 9

1 9 1 3 9 3

8 18 10 4 10 364 = =

9 9 9 1 9 9

26 8 or 2

9 9

x x x

EXP

Evaluate Expressions Containing Variables

2

2

2( 7) 3 when 2 and 1

( 1) 2( 2 7) 3

1 2( 2 7) 3

1 2(5) 3

1 10 3

9 3

6

y x x y

HOMEWORK 19

Page 77 ndash 7818 21 29 35 43 57 61 75 79 83 87 95

EXP EXP

Examples

2

2

(14 2) 5(3 2)

(7) 5(1)

7 5(1)

7 5

12

29 72 8 3 5

9 72 8 9 5

9 9 9 5

9 81 5

90 5

85

EXP EXP

Examples

25 18 3

25 18 3

25 6

19

2( 5) 18 3

25 18 3

25 6

31

EXP

Examples

4 3 2

7 5 9

4 3

7

1

2

5 9

3

4 2 = 105

7 15

4 15 60 2 7 14 and

7 15 105 15 7 105

60 14

105 105

46

105

LCD

Examples

Write the following statement as mathematical expressions using parentheses and brackets and then evaluate

Multiply 9 by 6 add 7 to this product Subtract 12 from the sum Divide this difference by 5

[[(9 6) + 7] ndash 12] divide 5

495

EXP

EXP

EXP

Evaluate Expressions Containing Variables

8 7 when 4

8(4) 732 725

x x

2

2 when 9

9 (9)(9) 81x x

2

2 when 9

9 (9)(9) 81x x

EXP

EXP

Evaluate Expressions Containing Variables

2

2 when 6

( 6) ( 6)( 6) 36y y

2

2 when 6

( 6) ( 6)( 6) 36y y

EXP

Evaluate Expressions Containing Variables

2

2

22 3 4 when

3

2 2 4 22 3 4 = 2 3 4

3 3 9 3

2 4 3 2 8 64 = 4 LCD = 9

1 9 1 3 9 3

8 18 10 4 10 364 = =

9 9 9 1 9 9

26 8 or 2

9 9

x x x

EXP

Evaluate Expressions Containing Variables

2

2

2( 7) 3 when 2 and 1

( 1) 2( 2 7) 3

1 2( 2 7) 3

1 2(5) 3

1 10 3

9 3

6

y x x y

HOMEWORK 19

Page 77 ndash 7818 21 29 35 43 57 61 75 79 83 87 95

EXP EXP

Examples

25 18 3

25 18 3

25 6

19

2( 5) 18 3

25 18 3

25 6

31

EXP

Examples

4 3 2

7 5 9

4 3

7

1

2

5 9

3

4 2 = 105

7 15

4 15 60 2 7 14 and

7 15 105 15 7 105

60 14

105 105

46

105

LCD

Examples

Write the following statement as mathematical expressions using parentheses and brackets and then evaluate

Multiply 9 by 6 add 7 to this product Subtract 12 from the sum Divide this difference by 5

[[(9 6) + 7] ndash 12] divide 5

495

EXP

EXP

EXP

Evaluate Expressions Containing Variables

8 7 when 4

8(4) 732 725

x x

2

2 when 9

9 (9)(9) 81x x

2

2 when 9

9 (9)(9) 81x x

EXP

EXP

Evaluate Expressions Containing Variables

2

2 when 6

( 6) ( 6)( 6) 36y y

2

2 when 6

( 6) ( 6)( 6) 36y y

EXP

Evaluate Expressions Containing Variables

2

2

22 3 4 when

3

2 2 4 22 3 4 = 2 3 4

3 3 9 3

2 4 3 2 8 64 = 4 LCD = 9

1 9 1 3 9 3

8 18 10 4 10 364 = =

9 9 9 1 9 9

26 8 or 2

9 9

x x x

EXP

Evaluate Expressions Containing Variables

2

2

2( 7) 3 when 2 and 1

( 1) 2( 2 7) 3

1 2( 2 7) 3

1 2(5) 3

1 10 3

9 3

6

y x x y

HOMEWORK 19

Page 77 ndash 7818 21 29 35 43 57 61 75 79 83 87 95

EXP

Examples

4 3 2

7 5 9

4 3

7

1

2

5 9

3

4 2 = 105

7 15

4 15 60 2 7 14 and

7 15 105 15 7 105

60 14

105 105

46

105

LCD

Examples

Write the following statement as mathematical expressions using parentheses and brackets and then evaluate

Multiply 9 by 6 add 7 to this product Subtract 12 from the sum Divide this difference by 5

[[(9 6) + 7] ndash 12] divide 5

495

EXP

EXP

EXP

Evaluate Expressions Containing Variables

8 7 when 4

8(4) 732 725

x x

2

2 when 9

9 (9)(9) 81x x

2

2 when 9

9 (9)(9) 81x x

EXP

EXP

Evaluate Expressions Containing Variables

2

2 when 6

( 6) ( 6)( 6) 36y y

2

2 when 6

( 6) ( 6)( 6) 36y y

EXP

Evaluate Expressions Containing Variables

2

2

22 3 4 when

3

2 2 4 22 3 4 = 2 3 4

3 3 9 3

2 4 3 2 8 64 = 4 LCD = 9

1 9 1 3 9 3

8 18 10 4 10 364 = =

9 9 9 1 9 9

26 8 or 2

9 9

x x x

EXP

Evaluate Expressions Containing Variables

2

2

2( 7) 3 when 2 and 1

( 1) 2( 2 7) 3

1 2( 2 7) 3

1 2(5) 3

1 10 3

9 3

6

y x x y

HOMEWORK 19

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Examples

Write the following statement as mathematical expressions using parentheses and brackets and then evaluate

Multiply 9 by 6 add 7 to this product Subtract 12 from the sum Divide this difference by 5

[[(9 6) + 7] ndash 12] divide 5

495

EXP

EXP

EXP

Evaluate Expressions Containing Variables

8 7 when 4

8(4) 732 725

x x

2

2 when 9

9 (9)(9) 81x x

2

2 when 9

9 (9)(9) 81x x

EXP

EXP

Evaluate Expressions Containing Variables

2

2 when 6

( 6) ( 6)( 6) 36y y

2

2 when 6

( 6) ( 6)( 6) 36y y

EXP

Evaluate Expressions Containing Variables

2

2

22 3 4 when

3

2 2 4 22 3 4 = 2 3 4

3 3 9 3

2 4 3 2 8 64 = 4 LCD = 9

1 9 1 3 9 3

8 18 10 4 10 364 = =

9 9 9 1 9 9

26 8 or 2

9 9

x x x

EXP

Evaluate Expressions Containing Variables

2

2

2( 7) 3 when 2 and 1

( 1) 2( 2 7) 3

1 2( 2 7) 3

1 2(5) 3

1 10 3

9 3

6

y x x y

HOMEWORK 19

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EXP

EXP

EXP

Evaluate Expressions Containing Variables

8 7 when 4

8(4) 732 725

x x

2

2 when 9

9 (9)(9) 81x x

2

2 when 9

9 (9)(9) 81x x

EXP

EXP

Evaluate Expressions Containing Variables

2

2 when 6

( 6) ( 6)( 6) 36y y

2

2 when 6

( 6) ( 6)( 6) 36y y

EXP

Evaluate Expressions Containing Variables

2

2

22 3 4 when

3

2 2 4 22 3 4 = 2 3 4

3 3 9 3

2 4 3 2 8 64 = 4 LCD = 9

1 9 1 3 9 3

8 18 10 4 10 364 = =

9 9 9 1 9 9

26 8 or 2

9 9

x x x

EXP

Evaluate Expressions Containing Variables

2

2

2( 7) 3 when 2 and 1

( 1) 2( 2 7) 3

1 2( 2 7) 3

1 2(5) 3

1 10 3

9 3

6

y x x y

HOMEWORK 19

Page 77 ndash 7818 21 29 35 43 57 61 75 79 83 87 95

EXP

EXP

Evaluate Expressions Containing Variables

2

2 when 6

( 6) ( 6)( 6) 36y y

2

2 when 6

( 6) ( 6)( 6) 36y y

EXP

Evaluate Expressions Containing Variables

2

2

22 3 4 when

3

2 2 4 22 3 4 = 2 3 4

3 3 9 3

2 4 3 2 8 64 = 4 LCD = 9

1 9 1 3 9 3

8 18 10 4 10 364 = =

9 9 9 1 9 9

26 8 or 2

9 9

x x x

EXP

Evaluate Expressions Containing Variables

2

2

2( 7) 3 when 2 and 1

( 1) 2( 2 7) 3

1 2( 2 7) 3

1 2(5) 3

1 10 3

9 3

6

y x x y

HOMEWORK 19

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EXP

Evaluate Expressions Containing Variables

2

2

22 3 4 when

3

2 2 4 22 3 4 = 2 3 4

3 3 9 3

2 4 3 2 8 64 = 4 LCD = 9

1 9 1 3 9 3

8 18 10 4 10 364 = =

9 9 9 1 9 9

26 8 or 2

9 9

x x x

EXP

Evaluate Expressions Containing Variables

2

2

2( 7) 3 when 2 and 1

( 1) 2( 2 7) 3

1 2( 2 7) 3

1 2(5) 3

1 10 3

9 3

6

y x x y

HOMEWORK 19

Page 77 ndash 7818 21 29 35 43 57 61 75 79 83 87 95

EXP

Evaluate Expressions Containing Variables

2

2

2( 7) 3 when 2 and 1

( 1) 2( 2 7) 3

1 2( 2 7) 3

1 2(5) 3

1 10 3

9 3

6

y x x y

HOMEWORK 19

Page 77 ndash 7818 21 29 35 43 57 61 75 79 83 87 95

HOMEWORK 19

Page 77 ndash 7818 21 29 35 43 57 61 75 79 83 87 95