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

(Marvins-Underground-K-12) #1
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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.





(

3

4

) 3





(

1

4

) 4





23

22





34

36





(

5

6

)− 2





52

53





85

86





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

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

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