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 46: 104



Work Step by Step

RECALL: $\sqrt[n]{a^m} = a^{\frac{m}{n}}.$ Use the rule above to obtain $x^{\frac{12}{4}} \\=x^{3}.$ Note, however, that $x$ can be any real number. This means that when $x$ is negative, $x^3$ is also negative. Since the principal fourth root of an expression is nonegative, the answer above must be adjusted to $|x^3|.$ Thus, $\sqrt[4]{x^{12}} = |x^3|.$
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