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