Intermediate Algebra (12th Edition)

Published by Pearson
ISBN 10: 0321969359
ISBN 13: 978-0-32196-935-4

Chapter 7 - Section 7.3 - Simplifying Radicals, the Distance Formula, and Circles - 7.3 Exercises - Page 459: 43



Work Step by Step

The quotient rule for radicals tells us that $\sqrt[n] \frac{a}{b}=\frac{\sqrt[n] a}{\sqrt[n] b}$ (if $\sqrt[n] a$ and $\sqrt[n] b$ are real numbers and $n$ is a natural number). That is, the nth root of a quotient is the quotient of the nth roots. Therefore, $\sqrt[5] \frac{1}{x^{15}}=\frac{\sqrt[5] 1}{\sqrt[5] x^{15}}=\frac{1}{x^{3}}$. $\sqrt[5] 1=1$, because $1^{5}=1$ $\sqrt[5] x^{15}=x^{3}$, because $(x^{3})^{5}=x^{3\times5}=x^{15}$
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