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: 35

Answer

$\frac{p^{3}}{9}$

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, $\sqrt \frac{p^{6}}{81}=\frac{\sqrt p^{6}}{\sqrt 81}=\frac{p^{3}}{9}$. $\sqrt p^{6}=p^{3}$, because $(p^{3})^{2}=p^{3\times2}=p^{6}$ $\sqrt 81=9$, because $9^{2}=81$
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