Chapter 5 e X P O N e N T S a N D r O O T S 107

DeMYSTiFieD / algebra DeMYSTiFieD / HuttenMuller / 000-0 / Chapter 5

Property 8 ab a

b

n n

n









=

Property 8 says that we can take the quotient followed by the power or each
power followed by the quotient.

EXAMPLES

Use Property 8 to rewrite the expression.

2

5

2

5

2

5

2

5

2

5

8

125

(^33)
3




=⋅⋅= =
x
y
x
y





 =
(^44)
4
x
y
x
y
x
y
2
5
(^424)
54
8
20





 ==()()
We can combine Properties 6 and 8 to help us rewrite a quotient raised to a
negative power.
Property 9
ab b
a
n n
n





−
Here is why it is true.
a
b
a
b
a
b
 nnn






















−−() 11 () − bb
a
b
a
n n
n





We will use Property 9 for the rest of the examples and practice problems
that involve fractions and negative exponents.
EXAMPLES
Simplify and eliminate any negative exponent.
2
3
3
2
9
4
(^22)
2





−
EXAMPLES
Use Property 8 to rewrite the expression.
EXAMPLES
Use Property 8 to rewrite the expression.
EXAMPLES
Simplify and eliminate any negative exponent.
EXAMPLES
Simplify and eliminate any negative exponent.