College Algebra (11th Edition)

Published by Pearson
ISBN 10: 0321671791
ISBN 13: 978-0-32167-179-0

Chapter R - Section R.6 - Rational Exponents - R.6 Exercises - Page 57: 56

Answer

$\dfrac{1000}{1331}$

Work Step by Step

Using $a^{-x}=\dfrac{1}{a^x}$ or $\dfrac{1}{a^{-x}}=a^x$, the given expression, $ \left( \dfrac{121}{100} \right)^{-3/2} ,$ simplifies to \begin{array}{l}\require{cancel} \dfrac{1}{\left( \dfrac{121}{100} \right)^{3/2}} \\\\= \left( \dfrac{100}{121} \right)^{3/2} .\end{array} Using $a^{m/n}=\sqrt[n]{a^m}=(\sqrt[n]{a})^m$, the expression, $ \left( \dfrac{100}{121} \right)^{3/2} $, simplifies to \begin{array}{l}\require{cancel} \left(\sqrt[]{\dfrac{100}{121}} \right)^3 \\\\= \left(\sqrt[]{\left( \dfrac{10}{11} \right)^2} \right)^3 \\\\= \left( \dfrac{10}{11} \right)^3 \\\\= \dfrac{1000}{1331} .\end{array}
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.