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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. 126 (page 786)

In the following exercises, write with a rational exponent.
$鈸� \sqrt[4]{5 x} 鈸� \sqrt[8]{9 y} 鈸� 7 \sqrt[5]{3 z}$

Short Answer

Expert verified

Part (a). $\sqrt[4]{5 x} = {(5 x)}^{\frac{1}{4}}$

Part (b). $\sqrt[8]{9 y} = {(9 y)}^{\frac{1}{8}}$

Part (c). $7 \sqrt[5]{3 z} = 7 {(3 z)}^{\frac{1}{5}}$

Step by step solution

01

Part (a) Step 1. Rational exponent of 5x4

We know that, $\sqrt[n]{a} = a^{\frac{1}{n}}$

The index is $4$

The denominator of the exponent will be $4$ .

role="math" localid="1644750007013" $\sqrt[4]{5 x} = {(5 x)}^{\frac{1}{4}}$

02

Part (b) Step 1. Rational exponent of 9y8

We know that, $\sqrt[n]{a} = a^{\frac{1}{n}}$

The index is $8$

The denominator of the exponent will be $8$ .

role="math" localid="1644750026382" $\sqrt[8]{9 y} = {(9 y)}^{\frac{1}{8}}$

03

Part (c) Step 1. Rational exponent of 73z5

We know that, $\sqrt[n]{a} = a^{\frac{1}{n}}$

The index is $5$

The denominator of the exponent will be $5$

role="math" localid="1644750055676" $7 \sqrt[5]{3 z} = 7 {(3 z)}^{\frac{1}{5}}$

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Most popular questions from this chapter

Simplify:

(a) ${(- 64)}^{- \frac{1}{2}}$

(b) ${- 64}^{\frac{1}{2}}$

(c) ${(64)}^{- \frac{1}{2}}$

Explain why $\sqrt[4]{- 64}$ is not a real number but $\sqrt[3]{- 64}$ is.

Simplify:

$(a) 5 + \sqrt{75} (b) \frac{10 - \sqrt{75}}{5} .$

In the following exercises, solve.

$\sqrt[3]{6 x + 4} = 4$

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(a) $\sqrt{\frac{45 r^{3}}{s^{10}}}$

(b) $\sqrt[3]{\frac{625 u^{10}}{v^{3}}}$

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