College Algebra (6th Edition)

Published by Pearson
ISBN 10: 0-32178-228-3
ISBN 13: 978-0-32178-228-1

Chapter P - Prerequisites: Fundamental Concepts of Algebra - Exercise Set P.3: 107

Answer

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

Work Step by Step

$$\sqrt[9]{x^6y^3}$$ To convert from a radical expression to an expression with a rational exponent, the exponent becomes the numerator, and the index becomes the denominator: $$=x^\frac{6}{9}y^\frac{3}{9}$$ Simplify all fractions: $$=x^\frac{2}{3}y^\frac{1}{3}$$ Convert back to a radical expression - the numerator becomes the exponent, the denominator becomes the index: $$=\sqrt[3]{x^2y}$$
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