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: 107

Answer

$\sqrt[3]{x^2y}$

Work Step by Step

RECALL: (i) $\sqrt[n]{a} = a^{\frac{1}{n}}.$ (ii) $(a^m)^n=a^{mn}.$ Use rule (i) above to obtain $(x^6y^3)^{\frac{1}{9}}.$ Use rule (ii) above to obtain $x^{\frac{6}{9}}y^{\frac{3}{9}} \\=x^{\frac{2}{3}}y^{\frac{1}{3}} \\=(x^2y)^{\frac{1}{3}}.$ Write the expression in radical form using rule (i) above to obtain $\sqrt[3]{x^2y}.$
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