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: 44

Answer

$\frac{2}{y^{4}}$

Work Step by Step

he 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, $\sqrt[5]\frac{32}{y^{20}}=\frac{\sqrt[5]32}{\sqrt[5]y^{20}}=\frac{2}{y^{4}}$. $\sqrt[5] 32=2$, because $2^{5}=32$ $\sqrt[5] y^{20}=y^{4}$, because $(y^{4})^{5}=y^{4\times5}=y^{20}$
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