Intermediate Algebra (6th Edition)

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

Chapter 7 - Review: 45



Work Step by Step

We are given the expression $(a^{\frac{1}{2}}a^{-2})^{3}$. First, we can use the product rule to simplify, which holds that $a^{m}\times a^{n}=a^{m+n}$ (where a is a real number, and m and n are positive integers). $(a^{\frac{1}{2}+(-2)})^{3}=(a^{-\frac{3}{2}})^{3}$ Next, we can use the power rule, which holds that $(a^{m})^{n}=a^{m\times n}$ (where a is a real number, and m and n are integers). $(a^{-\frac{3}{2}})^{3}=a^{-\frac{3}{2}\times3}=a^{-\frac{9}{2}}=\frac{1}{a^{\frac{9}{2}}}$
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.