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: 37

Answer

$-\frac{3}{4}$

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, $\sqrt[3] \frac{-27}{64}=\frac{\sqrt[3] (-27)}{\sqrt[3] 64}=\frac{-3}{4}=-\frac{3}{4}$. $\sqrt[3] -27=-3$, because $(-3)^{3}=-27$ $\sqrt[3] 64=4$, because $4^{3}=64$
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.