College Algebra (11th Edition)

Published by Pearson
ISBN 10: 0321671791
ISBN 13: 978-0-32167-179-0

Chapter R - Section R.6 - Rational Exponents - R.6 Exercises - Page 58: 87

Answer

$z^{-1/2} \left( 9+2z^{} \right)$

Work Step by Step

Factoring the given factor, $ z^{-1/2} ,$ then the given expression, $ 9z^{-1/2}+2z^{1/2} ,$ is equivalent to \begin{array}{l}\require{cancel} z^{-1/2} \left( \dfrac{9z^{-1/2}}{z^{-1/2}}+\dfrac{2z^{1/2}}{z^{-1/2}} \right) \\\\= z^{-1/2} \left( 9z^{-\frac{1}{2}-\left(-\frac{1}{2}\right)}+2z^{\frac{1}{2}-\left(-\frac{1}{2}\right)} \right) \\\\= z^{-1/2} \left( 9z^{-\frac{1}{2}+\frac{1}{2}}+2z^{\frac{1}{2}+\frac{1}{2}} \right) \\\\= z^{-1/2} \left( 9z^{0}+2z^{1} \right) \\\\= z^{-1/2} \left( 9(1)+2z^{} \right) \\\\= z^{-1/2} \left( 9+2z^{} \right) .\end{array}
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