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: 76

Answer

$\frac{5}{3}x^{\frac{11}{15}}$

Work Step by Step

We will use the rule $\frac{a^{m}}{a^{n}}=a^{m-n}$ in the simplification of the expression: $\frac{5x^{\frac{2}{5}}}{3x^{-\frac{1}{3}}}$ $=\frac{5}{3}\times\frac{x^{\frac{2}{5}}}{x^{-\frac{1}{3}}}$ $=\frac{5}{3}\times x^{\frac{2}{5}+(\frac{1}{3})}$ $=\frac{5}{3}\times x^{\frac{2(3)+1(5)}{15}}$ $=\frac{5}{3}\times x^{\frac{6+5}{15}}$ $=\frac{5}{3}\times x^{\frac{11}{15}}$ $=\frac{5}{3}x^{\frac{11}{15}}$
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