7-5 Division Properties of
Exponents
Algebra 1
Quotient of Powers Property

To divide powers having the same base,
subtract exponents.
•
Let a & b be numbers and let m and n be integers.
am
m n

a
though a  0
n
a
Example1

3
5
6

6
a.)
69
b.)
2
2
x
4
x
Power of a quotient property

To find the power of a quotient, find the power
of the numerator and the power of the
denominator and divide.
•
Let a & b be numbers and let m and n be integers.
m
m
a
a
 
   m though b  0
b
b
Example 2


Simplify the expression.
2
4
 
a.)
b.)

 
 x
3
 
2
4
Example 3


Simplify the expression.
3
2 2
a.) 3x y 12 x y
b.)

4x
y3
 3x

 y
2



3
Example 4

A middle-range weekly wage for a man in the
U.S. from 1980 to 1997 can be modeled by
t
y  460(1.035) where t=0 represents the
year 1990. Find the ratio of weekly earnings in
1997 to the earnings in 1980.