Intermediate Algebra (6th Edition)

Published by Pearson
ISBN 10: 0321785045
ISBN 13: 978-0-32178-504-6

Chapter 7 - Section 7.3 - Simplifying Radical Expressions - Exercise Set: 50

Answer

$-3z\sqrt[5] (z^{4})$

Work Step by Step

$\sqrt [5] (-243z^{9})=\sqrt [5] (-243\times z^{5}\times z^{4})$ $=\sqrt [5] (-243)\times \sqrt[5] (z^{5})\times \sqrt[5] (z^{4})=-3z\sqrt[5] (z^{4})$ We know that $\sqrt[5] (-243)=-3$, because $(-3)^{5}=-243$ and also that $\sqrt[5] (z^{5})=z$, because $(z)^{5}=z^{5}$.
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