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: 80

Answer

$-y\sqrt[3]{3x}$

Work Step by Step

Simplify each radicand to obtain $\sqrt[3]{(8y^3)(3x)}-y\sqrt[3]{27(3x)} \\=\sqrt[3]{(2y)^3(3x)}-y\sqrt[3]{3^3(3x)} \\=2y\sqrt[3]{3x} - y\cdot 3\sqrt [3]{3x} \\=2y\sqrt[3]{3x}-3y\sqrt[3]{3x}.$ RECALL: The distributive property states that for any real numbers a, b, and c, $ac + bc = (a+b)c \\ac - bc = (a-b)c.$ Use the distributive to obtain $(2y-3y)\sqrt[3]{3x} \\=-y\sqrt[3]{3x}.$
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