Algebra 2: Section 6.1Algebra 2: Section 6.1

Properties of ExponentsProperties of Exponents

Properties of ExponentsProperties of Exponents

Product of PowersProduct of Powers– (when multiplying (when multiplying

like bases, add like bases, add exponents)exponents)

Power of a PowerPower of a Power– (when taking an (when taking an

exponent to a exponent to a power, multiply the power, multiply the exponents)exponents)

m n m na a a

( )m n mna a

Properties of ExponentsProperties of Exponents

Power of a ProductPower of a Product– (distribute)(distribute)

Negative ExponentNegative Exponent– (flip to opposite (flip to opposite

side)side)

( )m m mab a b

1mm

aa

Properties of ExponentsProperties of Exponents

Zero ExponentZero Exponent– ((anythinganything taken to taken to

the zero power is 1)the zero power is 1)

Quotient of PowersQuotient of Powers– (when dividing like (when dividing like

bases, subtract bases, subtract exponents)exponents)

0 1a

mm n

n

aa

a

Properties of ExponentsProperties of Exponents

Power of a Power of a QuotientQuotient– (distribute)(distribute)

m m

m

a a

b b

Rules for Simplifying Exponential Rules for Simplifying Exponential ExpressionsExpressions

NO negative exponentsNO negative exponents

Simplify all numbers taken to a Simplify all numbers taken to a powerpower

Variables go in Variables go in alphabeticalphabetic order order

Only one occurrence of each Only one occurrence of each variable in a single termvariable in a single term

Examples:Examples:4 21. (3 ) 83 6561

35

2. 8

3

3

5

8

125

512

-3 93. (-2) ( 2) 6( 2) 64

Examples:Examples:32

3

a4.

b

6

9

a

b 6 9a b

2 5 2 125. ( )y y y 10 10y y

1

2

1 36.

( )

rs

rs

2

3 3

rs

r s

5

2

s

r

0y

2 3

3

rs s

r

Examples:Examples:6 3

3 157.

a b

a b 9

12

a

b

6 3 3

15

a b a

b

MOREMORE Examples: Examples:

2 4 38. 2 4ab a b c

2 39. 6x y xyz

11

510.

x

x

15

2211.

y

y

5 58a b c

3 46x y z

6x 7

1

y

MORE Examples:MORE Examples:

3412. x

43 213. 2a b

23

6 3

314.

6

x y

x y

34

15.n

12x3

64

n

12 816a b

6 8

4

x y

HomeworkHomework

p.326 p.326 #16-46 evens #16-46 evens