Quotient of Powers Property

To divide powers having the same base, subtract exponents.

0, aaa

a nmn

m

Example 1 Use the quotient of powers property

a.

86=

84

810

= 810 – 4

( )11 – 45–=

( )75–=

=( )115–( )45–

b.( )45–

1( )115–•

Power of a Quotient Property

To find a power of a quotient, find the power of the numerator and the power of the denominator and divide.

Example 2 Use the power of a quotient property

Simplify the expression.

a. 6

5 2

b. 3

2 3–

Power of a quotient property

SOLUTION

a. 6

5 2

=62

52

Place negative sign in numerator.b. 3

2 3– =

3

2 3–

=33

2 3–( )Power of a quotient property

Summary of Exponent Properties

Quotient of Power:

Power of a Quotient:

0, aaa

a nmn

m

Example 3 Use the quotient of powers property

b.x2

x3y=x2

x3

1

y•

x3 – 2 • y=

xy=

a.x3

x7

= x7 – 3

x4=

Example 4 Use the power of a quotient property

Simplify the expression.

a. yx 5

b. x

7 2–

=x2

7 2–( )Power of a quotient property

b.

Place negative sign in numerator.=x

7 2–x

7 2–

Power of a quotient property=y5

x5

a.

SOLUTION

yx 5

Example 4 Use the power of a quotient property

=x2

49Simplify.

Example 5 Use properties of exponents

a. 5y

4x2 3

=5y

4x2 3( )

( )3Power of a quotient property

=53y3

x2 3( )43 •Power of a product property

=125y3

64x6

Power of a power property

b.

b

a2 5

2a2

1• Power of a quotient property=

( )a2 5

b5 2a2

1•

Example 5 Use properties of exponents

Power of a power property=2a2

1•

b5

a10

Multiply fractions.=2a2 b5

a10

Quotient of powers property=2b5

a8

8.2 Warm-up (Day 1)Simplify the expression. Write your answer using

exponents.

1) 2)

3) 4)

5)

8.2 Warm-up (Day 2)Simplify the expression. Write your answer using

exponents.

1) 2)

3) 4)

5)