College Algebra (6th Edition)

Published by Pearson
ISBN 10: 0-32178-228-3
ISBN 13: 978-0-32178-228-1

Chapter P - Prerequisites: Fundamental Concepts of Algebra - Exercise Set P.3: 111

Answer

$\frac{1}{7} {x^{2}}{y^{-\frac{3}{2}}}$

Work Step by Step

$(49x^{-2}y^{4})^{-\frac{1}{2}}$ (x$y^{\frac{1}{2}}$) = $\frac{(xy^{\frac{1}{2}})}{(49x^{-2}y^{4})^{\frac{1}{2}}}$ = $\frac{(xy^{\frac{1}{2}})}{(49^{\frac{1}{2}}x^{-2\times\frac{1}{2}}y^{4\times\frac{1}{2}})}$ = $\frac{(xy^{\frac{1}{2}})}{(\sqrt 49 x^{-1}y^{2})}$ = $\frac{(x^{1+1})}{(7 y^{2-\frac{1}{2}})}$ = $\frac{(x^{2})}{7 (y^{\frac{3}{2}})}$ = $\frac{1}{7}\times\frac{x^{2}}{y^{\frac{3}{2}}}$ =$\frac{1}{7} {x^{2}}{y^{-\frac{3}{2}}}$
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