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Evaluating Algebraic Expressions
4-1 Exponents
Warm Up
California StandardsCalifornia Standards
Lesson Presentation
PreviewPreview
Evaluating Algebraic Expressions
4-1 Exponents
Warm UpFind the product.
6251. 5 • 5 • 5 • 5
2. 3 • 3 • 3
3. (–7) • (–7) • (–7)
4. 9 • 9
27
–343
81
Evaluating Algebraic Expressions
4-1 Exponents
AF2.1 Interpret positive whole-number powers as repeated multiplication and negative whole-number powers as repeated division or multiplication by the multiplicative inverse. Simplify and evaluate expressions that include exponents.Also covered: AF1.2
California Standards
Evaluating Algebraic Expressions
4-1 Exponents
Vocabulary
exponential form
exponent
base
power
Evaluating Algebraic Expressions
4-1 Exponents
If a number is in exponential form, the exponent represents how many times the base is to be used as a factor. A number produced by raising a base to an exponent is called a power. 27 and 33 are equivalent.
7
ExponentBase
2
Evaluating Algebraic Expressions
4-1 Exponents
Identify how many times 4 is a factor.4 • 4 • 4 • 4 = 44
Write in exponential form.
Additional Example 1: Writing Exponents
A. 4 • 4 • 4 • 4
Read (–6)3 as “–6 to the 3rd power" or "–6 cubed”.
Reading Math
Identify how many times –6 is a factor.
(–6) • (–6) • (–6) = (–6)3
B. (–6) • (–6) • (–6)
Evaluating Algebraic Expressions
4-1 Exponents
Identify how many times 5 and d are each used as a factor.
Additional Example 1: Writing Exponents
C. 5 • 5 • d • d • d • d
Write in exponential form.
5 • 5 • d • d • d • d = 52d4
Evaluating Algebraic Expressions
4-1 Exponents
Identify how many times x is a factor.x • x • x • x • x = x5
Write in exponential form.
Check It Out! Example 1
A. x • x • x • x • x
Identify how many times d is a factor.
d • d • d = d3
B. d • d • d
Evaluating Algebraic Expressions
4-1 Exponents
Identify how many times 7 and b are each used as a factor.
7 • 7 • b • b = 72b2
Check It Out! Example 1
C. 7 • 7 • b • b
Write in exponential form.
Evaluating Algebraic Expressions
4-1 Exponents
A. 35
= 243
35 = 3 • 3 • 3 • 3 • 3 Find the product.
Find the product.
B.
Simplify.
Additional Example 2: Simplifying Powers
= 1
27
Evaluating Algebraic Expressions
4-1 Exponents
D. –28
= 256
–28 = –(2 • 2 • 2 • 2 • 2 • 2 • 2 • 2)
= –256
= (–4) • (–4) • (–4) • (–4) (–4)4
C. (–4)4
Simplify.
Additional Example 2: Simplifying Powers
Find the product.
Find the product. Then make the answer negative.
Evaluating Algebraic Expressions
4-1 Exponents
The expression (–4)4 is not the same as the expression –44. Think of –44 as –1 ● 44. By the order of operations, you must evaluate the exponent before multiplying by –1.
Caution!
Evaluating Algebraic Expressions
4-1 Exponents
A. 74
= 240174 = 7 • 7 • 7 • 7 Find the product.
Simplify.
Check It Out! Example 2
Find the product.
B.
= 1 8
Evaluating Algebraic Expressions
4-1 Exponents
D. –94
= 25
–94 = –(9 • 9 • 9 • 9)
= –6,561
= (–5) • (–5) (–5)2
C. (–5)2
Evaluate.
Find the product.
Find the product. Then make the answer negative.
Check It Out! Example 2
Evaluating Algebraic Expressions
4-1 ExponentsAdditional Example 3: Using the Order of Operations
4(7) + 16
Substitute 4 for x, 2 for y, and 3 for z.
Simplify the powers.
Subtract inside the parentheses.
Multiply from left to right.
4(24 – 32) + 42
4(16 – 9) + 16
28 + 16
Evaluate x(yx – zy) + x for x = 4, y = 2, and z = 3.
y
x(yx – zy) + xy
Add. 44
Evaluating Algebraic Expressions
4-1 ExponentsCheck It Out! Example 3
60 – 7(7)
Substitute 5 for x, 2 for y, and 60 for z.
Simplify the powers.
Subtract inside the parentheses.
Multiply from left to right.
60 – 7(25 – 52)
60 – 7(32 – 25)
60 – 49
Evaluate z – 7(2x – xy) for x = 5, y = 2, and z = 60.z – 7(2x – xy)
Subtract. 11
Evaluating Algebraic Expressions
4-1 Exponents
(72 – 3 • 7)1
2
Additional Example 4: Geometry Application
Simplify inside the parentheses.
Multiply.
Substitute the number of sides for n.
Subtract inside the parentheses.
14 diagonals
(49 – 21)1
2
(n2 – 3n)1
2
(28)1
2
Use the expression (n2 – 3n) to find the number of diagonals in a 7-sided figure.
1 2
Evaluating Algebraic Expressions
4-1 Exponents
A 7-sided figure has 14 diagonals. You can verify your answer by sketching the diagonals.
Additional Example 4 Continued
Evaluating Algebraic Expressions
4-1 Exponents
(42 – 3 • 4)1
2
Check It Out! Example 4
Simplify inside the parentheses.
Multiply
Substitute the number of sides for n.
Subtract inside the parentheses.
2 diagonals
(16 – 12)1
2
(n2 – 3n)1
2
(4)1
2
Use the expression (n2 – 3n) to find the number of diagonals in a 4-sided figure.
1 2
Evaluating Algebraic Expressions
4-1 Exponents
A 4-sided figure has 2 diagonals. You can verify your answer by sketching the diagonals.
Check It Out! Example 4 Continued
Evaluating Algebraic Expressions
4-1 ExponentsLesson Quiz
Write in exponential form.
1. n • n • n • n 2. (–8) • (–8) • (–8) • (h)
256
–213
(–8)3h
3. (–4)4
5. Evaluate xz – yx for x = 5, y = 3, and z = 6.
n4
6. A population of bacteria doubles in size every minute. The number of bacteria after 5 minutes is 15 25. How many are there after 5 minutes?480
Simplify.
4.