The Algebra Teacher\'s Guide to Reteaching Essential Concepts and Skills

Name Date

WORKSHEET 6.3: USING THE PROPERTIES OF EXPONENTS

THAT APPLY TO MULTIPLICATION AND DIVISION

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The properties of exponents are summarized below:

• Multiplication:xmxn=xm+n Example:^25 ·^2 −^8 =^2 −^3 =

1

23

=

1

8

• Power of a power:(xm)n=xmn Example:(3^2 )^3 =^32 ·^3 =^36 =^729


• Power of a product:(xy)m=xmym Example:(2·3)^2 = 22 · 32 = 4 · 9 = 36


• Division:

xm

xn

=xm−n;x= 0 Example:

23

2 −^1

= 23 −(−1)= 24 = 16

• Power of a quotient:

(

x

y

)m

=

xm

ym

;y= 0 Example:

(

2

3

) 2

=

22

32

=

4

9

DIRECTIONS: Simplify.

1. 22 · 24 2. 2 −^3 · 21 3.

52 · 51

53

4.(6−^1 )^2

5. (5·2)^3 6.

72

7 −^3

(

2

5

) 3

(

32 · 2

5

) 3

CHALLENGE:Mike used the power of a product property to simplify (2^3 ·3)^2 as

26 ·^32. Nicole used the order of operations and simplified (2^3 ·3)^2 as (8·3)^2

or 24^2. Who was correct? Explain your answer.

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Copyright

©

2011 by Judith A. Muschla, Gary Robert Muschla, and Erin Muschla. All rights reserved.