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: 99

Answer

$27y^{\frac{2}{3}}$

Work Step by Step

$\displaystyle \frac{(3y^{1/4})^{3}}{y^{1/12}}=\qquad$... apply $(ab)^{n}=a^{n}b^{n}$ $=\displaystyle \frac{(3^{3})(y^{1/4})^{3}}{y^{1/12}}$... apply $(a^{m})^{n}=a^{mn}$ $=\displaystyle \frac{27y^{3/4}}{y^{1/12}}\qquad$... apply $\displaystyle \frac{a^{m}}{a^{n}}=a^{m-n}$ ...$ \displaystyle \frac{3}{4}-\frac{1}{12}=\frac{9-1}{120}=\frac{8}{12}=\frac{2}{3}$ $=27y^{\frac{2}{3}}$
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