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: 72

Answer

$\frac{8}{a^{\frac{1}{12}}}$

Work Step by Step

We will use the rule $\frac{a^{m}}{a^{n}}=a^{m-n}$ in the simplification of the expression: $\frac{56a^{\frac{1}{6}}}{7a^{\frac{1}{4}}}$ $=\frac{56}{7}\times\frac{a^{\frac{1}{6}}}{a^{\frac{1}{4}}}$ $=8\times a^{\frac{1}{6}-(\frac{1}{4})}$ $=8\times a^{\frac{1(2)-1(3)}{12}}$ $=8\times a^{\frac{2-3}{12}}$ $=8\times a^{\frac{-1}{12}}$ $=\frac{8}{a^{\frac{1}{12}}}$
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