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: 90

Answer

$r^{-5/3} \left( 6r-5 \right)$

Work Step by Step

Factoring out the given factor, $ r^{-5/3} ,$ then the given expression, $ 6r^{-2/3}-5r^{-5/3} ,$ is equivalent to \begin{array}{l}\require{cancel} r^{-5/3} \left( \dfrac{6r^{-2/3}}{r^{-5/3}}-\dfrac{5r^{-5/3}}{r^{-5/3}} \right) \\\\= r^{-5/3} \left( 6r^{-\frac{2}{3}-\left(-\frac{5}{3}\right)}-5r^{-\frac{5}{3}-\left(-\frac{5}{3}\right)} \right) \\\\= r^{-5/3} \left( 6r^{-\frac{2}{3}+\frac{5}{3}}-5r^{-\frac{5}{3}+\frac{5}{3}} \right) \\\\= r^{-5/3} \left( 6r^{\frac{3}{3}}-5r^{0} \right) \\\\= r^{-5/3} \left( 6r^{1}-5(1) \right) \\\\= r^{-5/3} \left( 6r-5 \right) .\end{array}
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