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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. 8.60 (page 778)

Write with a rational exponent:
(a) $\sqrt[5]{a^{2}}$
(b) ${(\sqrt[3]{5 a b})}^{5}$
(c) $\sqrt{{(\frac{7 x y}{z})}^{3}}$

Short Answer

Expert verified

The rational exponent of $\sqrt[5]{a^{2}}$ is $a^{\frac{2}{5}}$

The rational exponent of ${(\sqrt[3]{5 a b})}^{5}$ is ${(5 a b)}^{\frac{5}{3}}$

The rational exponent of $\sqrt{{(\frac{7 x y}{z})}^{3}}$ is ${(\frac{7 x y}{z})}^{\frac{3}{2}}$

Step by step solution

01

Part (a) Step 1. Given

The radical expression $\sqrt[5]{a^{2}}$

To write the expression with a rational exponent.

02

Part (a) Step 2. Find numerator and denominator of exponent from the given expression

The numerator of the exponent is exponent, $2$ .

The denominator of the exponent is the index of the radical, $5$ .

So the rational exponent is ${(a)}^{\frac{2}{5}}$

03

Part (b) Step 1. Given

The radical expression ${(\sqrt[3]{5 a b})}^{5}$

To write the expression with a rational exponent.

04

Part (b) Step 2. Find numerator and denominator of exponent from the given expression

The numerator of the exponent is exponent, $5$ .

The denominator of the exponent is the index of the radical, $3$ .

So the rational exponent is ${(5 a b)}^{\frac{5}{3}}$

05

Part (c) Step 1. Given

The radical expression $\sqrt{{(\frac{7 x y}{z})}^{3}}$

To write the expression with a rational exponent.

06

Part (c) Step 2. Find numerator and denominator of exponent from the given expression

The numerator of the exponent is exponent, $3$ .

The denominator of the exponent is the index of the radical, $2$ .

So the rational exponent is ${(\frac{7 x y}{z})}^{\frac{3}{2}}$

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