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: 86

Answer

$5r^{-8} \left( r^{2}-2 \right)$

Work Step by Step

Factoring the given factor, $ 5r^{-8} ,$ then the given expression, $ 5r^{-6}-10r^{-8} ,$ is equivalent to \begin{array}{l}\require{cancel} 5r^{-8} \left( \dfrac{5r^{-6}}{5r^{-8}}-\dfrac{10r^{-8}}{5r^{-8}} \right) \\\\= 5r^{-8} \left( r^{-6-(-8)}-2r^{-8-(-8)} \right) \\\\= 5r^{-8} \left( r^{-6+8}-2r^{-8+8} \right) \\\\= 5r^{-8} \left( r^{2}-2r^{0} \right) \\\\= 5r^{-8} \left( r^{2}-2(1) \right) \\\\= 5r^{-8} \left( r^{2}-2 \right) .\end{array}
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