7-5 Division Properties of Exponents

Objectives

To divide powers with the same base

To raise a quotient to a power

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In the Solve It, the expression for the volume of the dowel involves a quotient raised to a power.

Essential Understanding You can use properties of exponents to divide powers with the same base.

You can use repeated multiplication to simplify quotients of powers with the same base. Expand the numerator and the denominator. Then divide out the common factors.

4 5 4 3 = 4 ⋅ 4 ⋅ 4 ⋅ 4 ⋅ 4 4 ⋅ 4 ⋅ 4 = 4 2 fraction 4 to the fifth , over 4 cubed end fraction . equals . fraction cross out enclosing , 4 , end crossout dot cross out enclosing , 4 , end crossout dot cross out enclosing , 4 , end crossout dot 4 dot 4 , over cross out enclosing , 4 , end crossout dot cross out enclosing , 4 , end crossout dot cross out enclosing , 4 , end crossout end fraction . equals , 4 squared

This example illustrates the following property of exponents.

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