Power of a Product and Power of a Quotient

Let a and b represent real numbers and m represent a positive integer.

Power of a Product Property

m m ma b a b

Power of a Quotient Property

, 0m m

m

a ab

b b

• Example 1

43x

Apply the power of a product property:

43x 4 43 x 481x

• Example 2

22 34x y

Apply the power of a product property:

22 34x y 2 22 2 34 x y

Now apply the power rule for exponents:

2 22 316 x y

4 616x y

• Example 33

3

x

Apply the power of a quotient property:

33

x

3

3

3

x 3

27

x

• Example 442

3

2x

y

Apply the power of a quotient property:

42

3

2x

y

42

43

2x

y

Now apply the power of a product property in the numerator:

42

43

2x

y

44 2

43

2 x

y

42

43

16 x

y

Now apply the power rule for exponents:

8

12

16x

y

42

43

16 x

y