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

Name Date

WORKSHEET 6.2: USING THE PROPERTIES OF EXPONENTS

THAT APPLY TO DIVISION

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There are two properties for working with exponents and division.

Property of exponents for division:To divide powers having the same base, subtract the

exponent in the denominator from the exponent in the numerator.

xm

xn

=xm−n x= 0

EXAMPLES

47

42

= 47 −^2 = 45 =1, 024

52

55

= 52 −^5 = 5 −^3 =

1

53

=

1

125

Property of exponents for a power of a quotient:To find the power of a quotient, find the

power of the numerator and the power of the denominator.

(

x

y

)m

=

xm

ym

y= 0

EXAMPLES

(

5

7

) 3

=

53

73

=

125

343

(

2

5

)− 4

=

2 −^4

5 −^4

=

54

24

=

625

16

DIRECTIONS: Rewrite each expression using the properties of exponents for division.

Then simplify each expression.

1. 
   

(

3

4

) 3

2. 
   

(

1

4

) 4

3. 
   

23

22

4. 
   

34

36

5. 
   

(

5

6

)− 2

6. 
   

52

53

7. 
   

85

86

8. 
   

3 −^2

34

CHALLENGE:Francine applied the property of exponents for division to

simplify

85

85

. She said that 8^5 −^5 = 80 =1. Phil said that

85

85

is a fraction

whose numerator and denominator are the same and therefore the

fraction is equal to 1. Who is correct? Explain your reasoning.

227

Copyright

©

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