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 - Page 30: 89


(a) $\frac{\sqrt[3]{x^{2}}}{x}$ (b) $\frac{\sqrt[6]{x}}{x}$ (c) $\frac{\sqrt[7]{x^{4}}}{x}$

Work Step by Step

(a) $\displaystyle \frac{1}{\sqrt[3]{x}}=\frac{1}{\sqrt[3]{x}} \displaystyle \frac{\sqrt[3]{x^{2}}}{\sqrt[3]{x^{2}}}=\frac{\sqrt[3]{x^{2}}}{x}$ (b) $\displaystyle \frac{1}{\sqrt[6]{x^{5}}}=\frac{1}{\sqrt[6]{x^{5}}} \displaystyle \frac{\sqrt[6]{x}}{\sqrt[6]{x}}=\frac{\sqrt[6]{x}}{x}$ (c) $\displaystyle \frac{1}{\sqrt[7]{x^{3}}}=\frac{1}{\sqrt[7]{x^{3}}} \displaystyle \frac{\sqrt[7]{x^{4}}}{\sqrt[7]{x^{4}}}=\frac{\sqrt[7]{x^4}}{\sqrt[7]{x^7}}=\frac{\sqrt[7]{x^{4}}}{x}$
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