Power of a Product Property of Exponents
Property —
Power of a Product Property of Exponents
English To raise a product to a power, you can first raise each
factor to the power. Then multiply.
Algebra (xy)n = xnyn (Here, n is a positive integer.)
Example (2x)3 = 23x3 = 8x3
Example 1
a. Use the Power of a Product Property of Exponents to simplify (3y)2.
b. Use the definition of exponential notation to justify your answer.
Solution
| a. Raise each factor to the power 2. |
(3y)2 |
= 32y2 = 9y2 |
| b. Rewrite the power to show
the factors. Then simplify. |
(3y)2 |
= (3y) · (3y)
= 3 · 3 ·
y · y
= 32y2
= 9y2 |
Example 2
Simplify: (23 · w5)4
Solution
| Use the Power of a Product Property
of Exponents to raise each factor inside
the parentheses to the power 4. |
(23
· w5)4 |
= (23)4(w5)4 |
| Use the Power of a Power Property
of Exponents. Simplify. |
|
= (23 · 4)(w5
· 4) = 212w20 |
Note:
We left 212 in exponential form. To
evaluate 212, use the “yx†key on a
scientific calculator or the “^†key
on a graphing calculator.
212 = 4096
|
