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: 92


$-3p^{-7/4} \left( p+10 \right)$

Work Step by Step

Factoring out the given factor, $ -3p^{-7/4} ,$ then the given expression, $ -3p^{-3/4}-30p^{-7/4} ,$ is equivalent to \begin{array}{l}\require{cancel} -3p^{-7/4} \left( \dfrac{-3p^{-3/4}}{-3p^{-7/4}}-\dfrac{30p^{-7/4}}{-3p^{-7/4}} \right) \\\\= -3p^{-7/4} \left( p^{-\frac{3}{4}-\left(-\frac{7}{4}\right)}+10p^{-\frac{7}{4}-\left(-\frac{7}{4}\right)} \right) \\\\= -3p^{-7/4} \left( p^{-\frac{3}{4}+\frac{7}{4}}+10p^{-\frac{7}{4}+\frac{7}{4}} \right) \\\\= -3p^{-7/4} \left( p^{\frac{4}{4}}+10p^{0} \right) \\\\= -3p^{-7/4} \left( p^{1}+10(1) \right) \\\\= -3p^{-7/4} \left( p+10 \right) .\end{array}
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