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: 56



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: $27^{4/3} = \left(27^{1/3}\right)^4$ Use rule (2) above to obtain: $=(\sqrt[3]{27})^4$ With $27=3^3$, the expression above is equivalent to: $=(\sqrt[3]{3^3})^4$ Use rule (3) above to obtain" $=(3)^4 \\=\color{blue}{81}$
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.