College Algebra 7th Edition

Published by Brooks Cole
ISBN 10: 1305115546
ISBN 13: 978-1-30511-554-5

Chapter P, Prerequisites - Section P.4 - Rational Exponents and Radicals - P.4 Exercises: 90

Answer

(a) $\displaystyle\frac{\sqrt[3]{x}}{x}$ (b) $\displaystyle\frac{\sqrt[4]{x}}{x}$ (c) $\displaystyle\frac{\sqrt[3]{x^{2}}}{x^{2}}$

Work Step by Step

(a) $\displaystyle \frac{1}{\sqrt[3]{x^{2}}}=\frac{1}{\sqrt[3]{x^{2}}} \displaystyle \frac{\sqrt[3]{x}}{\sqrt[3]{x}}=\frac{\sqrt[3]{x}}{x}$ (b) $\displaystyle \frac{1}{\sqrt[4]{x^{3}}}=\frac{1}{\sqrt[4]{x^{3}}} \displaystyle \frac{\sqrt[4]{x}}{\sqrt[4]{x}}=\frac{\sqrt[4]{x}}{x}$ (c) $\displaystyle \frac{1}{\sqrt[3]{x^{4}}}=\frac{1}{\sqrt[3]{x^{3}x}}=\frac{1}{x\sqrt[3]{x}}= \frac{1}{x\sqrt[3]{x}}\displaystyle \frac{\sqrt[3]{x^{2}}}{\sqrt[3]{x^{2}}} =\frac{\sqrt[3]{x^{2}}}{x\sqrt[3]{x^{3}}}=\frac{\sqrt[3]{x^{2}}}{x*x}=\frac{\sqrt[3]{x^{2}}}{x^{2}}$
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