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: 54

Answer

$(-64)^{1/4}$ is not a real number

Work Step by Step

RECALL: (1) $a^{1/4} = \sqrt[4]{a}$ (2) $\sqrt[4]{16} = 2$ since $2^4=16$ (3) For any real number $a$, $a^4 \ge 0$. Use rule (1) above to obtain: $(-64)^{1/4} = \sqrt[4]{-64}$ Note that there is no real number that when raised to the 4th power will give $-64$ since when a real number is raised to the 4th power, the result is always non-negative. Thus, $(-64)^{1/4}$ is not a real number
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