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Wednesday 29th of June
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 Depdendent Variable

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 Dependent Variable

 Number of inequalities to solve: 23456789
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Power of a Product Property of Exponents

Property â€” 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.

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) Â· (3y) = 3 Â· 3 Â· y Â· y = 32y2 = 9y2

Example 2

Simplify: (23 Â· w5)4

Solution

 Use the Power of a Product Property of Exponents to raise each factor inside the parentheses to the power 4. (23 Â· w5)4 = (23)4(w5)4 Use the Power of a Power Property of Exponents.Simplify. = (23 Â· 4)(w5 Â· 4)= 212w20

Note:

We left 212 in exponential form. To evaluate 212, use the â€œyxâ€ key on a scientific calculator or the â€œ^â€ key on a graphing calculator.

212 = 4096