College Algebra 7th Edition

Published by Brooks Cole
ISBN 10: 1305115546
ISBN 13: 978-1-30511-554-5

Chapter P, Prerequisites - Section P.4 - Rational Exponents and Radicals - P.4 Exercises: 30

Answer

$2a\sqrt[3]{a^2}$

Work Step by Step

The given radical can be written as: $=\sqrt[3]{8a^3 \cdot a^2} \\=\sqrt[3]{(2a)^3 \cdot a^2}$ RECALL: (i) $\sqrt[n]{b^n} = |b|$ when $n$ is even (ii) $\sqrt[n]{b^n} = b$ when $n$ is odd The given radical has n=3, which is odd. Use rule (ii) above to obtain: $=2a\sqrt[3]{a^2}$
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