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: 67


(a) $\frac{1}{x}$ (b) $\frac{xy^{4}}{8}$

Work Step by Step

(a) $(\frac{x^{-2/3}}{y^{1/2}})(\frac{x^{-2}}{y^{-3}})^{1/6}=x^{-2/3+-2*1/6}y^{-1/2-(-3)(1/6)}=\frac{1}{x}$ (b) $(\frac{x^{1/2}y^{2}}{2y^{1/4}})^{4}(\frac{4x^{-2}y^{-4}}{y^{2}})^{1/2}=x^{4*1/2}y^{2*4}2^{-1*4}y^{-1/4*4}4^{1/2}x^{-2*1/2}y^{-4*1/2}y^{-2*1/2}=x^2y^82^{-4}y^{-1}2x^{-1}y^{-2}y^{-1}=2^{-4+1}x^{2-1}y^{8-1-2-1}=\frac{xy^{4}}{8}$
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