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: 73

Answer

$\frac{4}{b^{\frac{5}{12}}}$

Work Step by Step

We will use the rule $\frac{a^{m}}{a^{n}}=a^{m-n}$ in the simplification of the expression: $\frac{48b^{\frac{1}{3}}}{12b^{\frac{3}{4}}}$ $=\frac{48}{12}\times\frac{b^{\frac{1}{3}}}{b^{\frac{3}{4}}}$ $=4\times b^{\frac{1}{3}-(\frac{3}{4})}$ $=4\times b^{\frac{1(4)-3(3)}{12}}$ $=4\times b^{\frac{4-9}{12}}$ $=4\times b^{\frac{-5}{12}}$ $=\frac{4}{b^{\frac{5}{12}}}$
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