Intermediate Algebra (6th Edition)

Published by Pearson
ISBN 10: 0321785045
ISBN 13: 978-0-32178-504-6

Chapter 7 - Section 7.2 - Rational Exponents - Exercise Set: 21

Answer

not a real number

Work Step by Step

We know that $a^{\frac{m}{n}}=(\sqrt[n] a)^{m}$ (where m and n are positive integers greater than 1 with $\frac{m}{n}$ in simplest form and $\sqrt[n] a$ is a real number). Therefore, $(-16)^{\frac{3}{4}}=(\sqrt[4] -16)^{3}$. However, $\sqrt[4] -16$ is not a real number, as we cannot find some number $b$ such that $b^{4}=-16$. In general, we cannot perform a radical function of a negative number when the index of the radical is even.
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.