Calculus with Applications (10th Edition)

Published by Pearson
ISBN 10: 0321749006
ISBN 13: 978-0-32174-900-0

Chapter R - Algebra Reference - R.6 Exponents - R.6 Exercises - Page R-25: 35


$\displaystyle \frac{4}{3}$

Work Step by Step

$[\displaystyle \frac{27}{64}]^{-1/3}=$ ...use: $(\displaystyle \frac{a}{b})^{m}=\frac{a^{m}}{b^{m}}$ $=\displaystyle \frac{27^{-1/3}}{64^{-1/3}}=$ ... recognize $64=4^{3}, 27=3^{3}$ $=\displaystyle \frac{(3^{3})^{-1/3}}{(4^{3})^{-1/3}}=$ ...use: $(a^{m})^{n}=a^{mn}$ $=\displaystyle \frac{3^{-1}}{4^{-1}}=$ ...use: $\displaystyle \frac{1}{a^{n}}=a^{-n}$ $=\displaystyle \frac{4}{3}$
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