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Properties of Exponents
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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

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