Precalculus (6th Edition)

Published by Pearson
ISBN 10: 013421742X
ISBN 13: 978-0-13421-742-0

Chapter R - Review of Basic Concepts - R.6 Rational Exponents - R.6 Exercises: 58

Answer

$\color{blue}{-27}$

Work Step by Step

RECALL: (1) $a^{m/n} = \left(^{1/n}\right)^m$ (2) $a^{1/n} = \sqrt[n]{a}$ (3) For positive real numbers $a$, $\sqrt[n]{a^n}=a$ Use rule (1) above to obtain: $-81^{3/4} = -\left(81^{1/4}\right)^3$ Use rule (2) above to obtain: $=-(\sqrt[4]{81})^3$ With $81=3^4$, the expression above is equivalent to: $=-(\sqrt[4]{3^4})^3$ Use rule (3) above to obtain" $=-(3)^3 \\=\color{blue}{-27}$
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