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: 71

Answer

$4x^{\frac{4}{15}}$

Work Step by Step

We will use the rule $\frac{a^{m}}{a^{n}}=a^{m-n}$ in the simplification of the expression: $\frac{24x^{\frac{3}{5}}}{6x^{\frac{1}{3}}}$ $=\frac{24}{6}\times\frac{x^{\frac{3}{5}}}{x^{\frac{1}{3}}}$ $=4\times x^{\frac{3}{5}-(\frac{1}{3})}$ $=4\times x^{\frac{3(3)-1(5)}{15}}$ $=4\times x^{\frac{9-5}{15}}$ $=4\times x^{\frac{4}{15}}$ $=4x^{\frac{4}{15}}$
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