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: 41

Answer

$-\frac{3}{x}$

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, $-\sqrt[4] \frac{81}{x^{4}}=-\frac{\sqrt[4] 81}{\sqrt[4] x^{4}}=-\frac{3}{x}$. $\sqrt[4] 81=3$, because $3^{4}=81$ $\sqrt[4] x^{4}=x$, because $(x)^{4}=x^{4}$
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