Elementary Algebra

Published by Cengage Learning
ISBN 10: 1285194055
ISBN 13: 978-1-28519-405-9

Chapter 11 - Additional Topics - 11.3 - Fractional Exponents - Problem Set 11.3: 78

Answer

$\frac{8a^{\frac{3}{4}}}{27}$

Work Step by Step

First, we will simplify the expression within the parenthesis using the rule $\frac{a^{m}}{a^{n}}=a^{m-n}$: $(\frac{2a^{\frac{1}{2}}}{3a^{\frac{1}{4}}})^{3}$ =$(\frac{2}{3}\times\frac{a^{\frac{1}{2}}}{a^{\frac{1}{4}}})^{3}$ =$(\frac{2}{3}\times a^{\frac{1}{2}-\frac{1}{4}})^{3}$ =$(\frac{2}{3}\times a^{\frac{2-1}{4}})^{3}$ =$(\frac{2}{3}\times a^{\frac{1}{4}})^{3}$ Now, we raise each term in the expression to the power of $3$: $(\frac{2}{3}\times a^{\frac{1}{4}})^{3}$ =$(\frac{2}{3})^{3}\times (a^{\frac{1}{4}})^{3}$ =$(\frac{2^{3}}{3^{3}})\times (a^{\frac{3}{4}})$ =$(\frac{8}{27})\times (a^{\frac{3}{4}})$ =$\frac{8a^{\frac{3}{4}}}{27}$
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