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: 36


$\displaystyle \frac{1000}{1331}$

Work Step by Step

$[\displaystyle \frac{121}{100}]^{-3/2}=$ ... recognize: 121$=11^{2}, $100$=10^{2}$ $=[\displaystyle \frac{11^{2}}{10^{2}}]^{-3/2}=$ ...use: $(\displaystyle \frac{a}{b})^{m}=\frac{a^{m}}{b^{m}}$ $=[(\displaystyle \frac{11}{10})^{2}]^{-3/2}=$ ...use: $(a^{m})^{n}=a^{mn}$ $=(\displaystyle \frac{11}{10})^{-3}=$ ...use: $\displaystyle \frac{1}{a^{n}}=a^{-n}$ $=(\displaystyle \frac{10}{11})^{3}=$ ...use: $(\displaystyle \frac{a}{b})^{m}=\frac{a^{m}}{b^{m}}$ $=\displaystyle \frac{10^{3}}{11^{3}}= \frac{1000}{1331}$
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