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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 8: Q. 8.67 (page 783)

Simplify:
a. ${(32 x^{\frac{1}{3}})}^{\frac{3}{5}}$ b. ${(x^{\frac{3}{4}} y^{\frac{1}{2}})}^{\frac{2}{3}}$

Short Answer

Expert verified

Part (a). The answer is $8 路 x^{\frac{1}{5}}$ .

part (b). The answer is $(x^{\frac{1}{2}} y^{\frac{1}{3}})$ .

Step by step solution

01

Part (a) Step 1. Simplifying

First, we use the Product to a Power

Property.

So,

${(32 x^{\frac{1}{3}})}^{\frac{3}{5}} {(32)}^{\frac{3}{5}} 路 {(x^{\frac{1}{3}})}^{\frac{3}{5}}$

To raise a power to a power, we multiply the exponents.

${(32)}^{\frac{3}{5}} 路 {(x^{\frac{1}{3}})}^{\frac{3}{5}} {(2^{5})}^{\frac{3}{5}} 路 {(x^{\frac{1}{3}})}^{\frac{3}{5}} [32 = 2^{5}] 2^{3} 路 x^{\frac{1}{5}} 8 路 x^{\frac{1}{5}} [2^{3} = 8]$

02

Part (b) Step 1. Simplifying the exponent

First, we use the Product to a

Power Property

${(x^{\frac{3}{4}} y^{\frac{1}{2}})}^{\frac{2}{3}} {(x^{\frac{3}{4}})}^{\frac{2}{3}} 路 {(y^{\frac{1}{2}})}^{\frac{2}{3}}$

To raise a power to a power, we multiply the exponents.

${(x^{\frac{3}{4}})}^{\frac{2}{3}} 路 {(y^{\frac{1}{2}})}^{\frac{2}{3}} (x^{\frac{1}{2}} y^{\frac{1}{3}})$

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Most popular questions from this chapter

In the following exercises, write as a radical expression.

$鈸� u^{\frac{1}{5}} 鈸� v^{\frac{1}{9}} 鈸� w^{\frac{1}{20}}$

In the following exercises, use the Product Property to simplify radical expression $\sqrt{125} .$

In the following exercises, simplify.

(a) $25^{\frac{3}{2}}$

(b) $9^{\frac{- 3}{2}}$

(c) ${(- 64)}^{\frac{2}{3}}$

Use the Quotient Property to simplify square roots.

(a) $\frac{\sqrt{72 n^{11}}}{\sqrt{2 n}}$

(b) $\sqrt[3]{\frac{162}{6}}$

(c) $\sqrt[4]{\frac{160 r^{10}}{5 r^{3}}}$

In the following exercises, solve.
$\sqrt{r - 1} = r - 1$

See all solutions

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