Intermediate Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-894-7
ISBN 13: 978-0-13417-894-3

Chapter 7 - Review Exercises - Page 576: 28

Answer

$y\sqrt[3]x$

Work Step by Step

Simplify. $\sqrt[9]{x^3y^{9}}$ Since, the power raised to a same exponent or base gets subtract when they are divide and the power raised to a each base gets add. As per definition of square root property,we have $(p)^{\frac{m}{n}}=(\sqrt[n] {p})^m$ Thus, the given radical term can be written as: $\sqrt[9]{x^3y^{9}}=\sqrt[9]{x^3}\sqrt[9]{y^{9}}$ or,$=x^{\frac{3}{9}}y^{\frac{9}{9}}$ or, $=x^\frac{1}{3}y$ Hence, $=y\sqrt[3]x$
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