Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter P - Section P.3 - Radicals and Rational Exponents - Exercise Set - Page 46: 113


$\displaystyle \frac{x^{3}}{y^{2}}$

Work Step by Step

$(\displaystyle \frac{x^{-5/4}y^{1/3}}{x^{-3/4}})^{-6}=(\frac{x^{-5/4}}{x^{-3/4}}\cdot y^{1/3})^{-6}\qquad$... apply $\displaystyle \frac{a^{m}}{a^{n}}=a^{m-n}$ $=(x^{-5/4-(-3/4)}\cdot y^{1/3})^{-6}$ ...$-\displaystyle \frac{5}{4}+\frac{3}{4}=\frac{-2}{4}=-\frac{1}{2}$ $=(x^{-1/2}y^{1/3})^{-6}\qquad$... apply $(ab)^{n}=a^{n}b^{n}$ $=x^{(-1/2)(-6)}y^{(1/3)(-6)}$ $=x^{3}y^{-2}\qquad$... apply $a^{-n}=\displaystyle \frac{1}{a^{n}}$ $=\displaystyle \frac{x^{3}}{y^{2}}$
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