Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter P - Section P.3 - Radicals and Rational Exponents - Exercise Set - Page 47: 125

Answer

See explanations.

Work Step by Step

Using the definition and exponential properties, we can rewrite the expression in several forms: $a^{\frac{m}{n}}=(a^{\frac{1}{n}})^m=(\sqrt[n] a)^m=\sqrt[n] {a^m}=(a^m)^{\frac{1}{n}}$, Thus the original term can mean "first raise $a$ to the $m$th power, then take the $n$th root", or vice versa.
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