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 - Page 63: 55



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: $8^{2/3} = \left(8^{1/3}\right)^2$ Use rule (2) above to obtain: $=(\sqrt[3]{8})^2$ With $8=2^3$, the expression above is equivalent to: $=(\sqrt[3]{2^3})^2$ Use rule (3) above to obtain" $=(2)^2 \\=\color{blue}{4}$
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