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: 75

Answer

3

Work Step by Step

We will use the rule $\frac{a^{m}}{a^{n}}=a^{m-n}$ in the simplification of the expression: $\frac{27n^{-\frac{1}{3}}}{9n^{-\frac{1}{3}}}$ $=\frac{27}{9}\times\frac{n^{-\frac{1}{3}}}{n^{-\frac{1}{3}}}$ $=3\times n^{-\frac{1}{3}+(\frac{1}{3})}$ $=3\times n^{\frac{-1+1}{3}}$ $=3\times n^{\frac{0}{3}}$ $=3\times n^{0}$ $=3\times 1$ $=3$
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