Power of a Quotient Property of Exponents

Property — Power of a Quotient Property of Exponents

English To raise a quotient to a power, you can first raise the numerator and denominator each to the power. Then divide.

Algebra (Here, n is a positive integer.)

Example

Example

a. Use the Power of a Quotient Property of Exponents to simplify

b. Use the definition of exponential notation to justify your answer.

Solution

a. Raise the numerator to the power 3. Raise the denominator to the power 3.
b. Rewrite the power to show the factors. Then simplify.