Intermediate Algebra (6th Edition)

Published by Pearson
ISBN 10: 0321785045
ISBN 13: 978-0-32178-504-6

Chapter 7 - Review - Page 470: 149



Work Step by Step

Using laws of exponents, the expression $ \dfrac{(x^{2/3}x^{-3})^3}{x^{-1/2}} $ simplifies to \begin{array}{l} \dfrac{x^{\frac{2}{3}\cdot3}x^{-3(3)}}{x^{-\frac{1}{2}}} \\\\= \dfrac{x^{2}x^{-9}}{x^{-\frac{1}{2}}} \\\\= x^{2+(-9)-\left( -\frac{1}{2} \right)} \\\\= x^{\frac{4-18+1}{2}} \\\\= x^{\frac{-13}{2}} \\\\= \dfrac{1}{x^{13/2}} .\end{array}
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