Algebra: A Combined Approach (4th Edition)

Published by Pearson
ISBN 10: 0321726391
ISBN 13: 978-0-32172-639-1

Chapter 10 - Review: 149

Answer

$\frac{1}{x^{\frac{13}{2}}}$

Work Step by Step

$\frac{(x^{\frac{2}{3}}x^{-3})^{3}}{x^{-\frac{1}{2}}}$ =$\frac{(x^{\frac{2}{3}-3})^{3}}{x^{-\frac{1}{2}}}$ =$\frac{(x^{\frac{2-3(3)}{3}})^{3}}{x^{-\frac{1}{2}}}$ =$\frac{(x^{\frac{2-9}{3}})^{3}}{x^{-\frac{1}{2}}}$ =$\frac{(x^{\frac{-7}{3}})^{3}}{x^{-\frac{1}{2}}}$ =$\frac{(x^{-\frac{7}{3}\times3})}{x^{-\frac{1}{2}}}$ =$\frac{x^{-7}}{x^{-\frac{1}{2}}}$ =$\frac{1}{x^{-\frac{1}{2}+7}}$ =$\frac{1}{x^{\frac{-1+14}{2}}}$ =$\frac{1}{x^{\frac{13}{2}}}$
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