Algebra 1: Common Core (15th Edition)

Published by Prentice Hall

Chapter 7 - Exponents and Exponential Functions - 7-5 Rational Exponents and Radicals - Lesson Check - Page 450: 8

Answer

The error is in the first step, for $27$ should also be raised to the power 2 under the root. The correct answer is $9\sqrt[3]{y^{2}}$.

Work Step by Step

The error is in the first step, for $27$ should also be raised to the power 2 under the root. $\sqrt[n]{a^{m}}=a^{m/n}$ $(27y)^{2/3}= \sqrt[3]{(27y)^{2}}$ $= \sqrt[3]{(3^{3}y)^{2}}$ $= \sqrt[3]{(3^{6})(y^{2})}$ $= \sqrt[3]{(3^{2})^{3}(y^{2})}$ $=3^{2}\sqrt[3]{y^{2}}$ $=9\sqrt[3]{y^{2}}$

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