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: 75

Answer

$2xy^{2} \sqrt[5]( x)^{2}$

Work Step by Step

$\frac{\sqrt[5] 64x^{10}y^{3}}{\sqrt[5] 2x^{3}y^{-7}}$ Using the product and quotient rules for exponents and radicals $= \sqrt[5] \frac{64x^{10}y^{3}}{2x^{3}y^{-7}}$ $= \sqrt[5](32 x^{10-3}. y^{3-(-7)})$ $= \sqrt[5]32 x^{7}. y^{10}$ $= \sqrt[5](2^{5}. x^{7}. y^{10})$ $=(2^{5}. x^{7}. y^{10})^{\frac{1}{5}} $ $=(2^{5}. x^{5}.x^{2}. y^{10})^{\frac{1}{5}} $ $=2xy^{2} \sqrt[5]( x^{2})$
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