Calculus with Applications (10th Edition)

Published by Pearson
ISBN 10: 0321749006
ISBN 13: 978-0-32174-900-0

Chapter R - Algebra Reference - R.6 Exponents - R.6 Exercises - Page R-25: 48


$ \displaystyle \frac{y^{2}}{x^{1/6}z^{5/4}}$

Work Step by Step

$ \displaystyle \frac{x^{3/2}\cdot y^{4/5}\cdot z^{-3/4}}{x^{5/3}\cdot y^{-6/5}\cdot z^{1/2}}=\qquad$ ....... use $\displaystyle \frac{a^{m}}{a^{n}}=a^{m-n}$ $=x^{3/2-(5/3)}\cdot y^{4/5-(-6/5)}\cdot z^{-3/4-(1/2)}$ ... simplify exponents: $...[\displaystyle \frac{3}{2}-\frac{5}{3}=\frac{3\cdot 3-5\cdot 2}{6}=-\frac{1}{6}]$ $...[-\displaystyle \frac{3}{4}-\frac{1}{2}=\frac{-3-1\cdot 2}{4}=-\frac{5}{4}]$ $=x^{-1/6}\cdot y^{2}\cdot z^{-5/4}\qquad$ ....... use $a^{-n}=\displaystyle \frac{1}{a^{n}}=(\frac{1}{a})^{n}$ $= \displaystyle \frac{y^{2}}{x^{1/6}z^{5/4}}$
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