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: 85


$4t^{-4} \left( t^{2}+2 \right)$

Work Step by Step

Factoring the given factor, $ 4t^{-4} ,$ then the given expression, $ 4t^{-2}+8t^{-4} ,$ is equivalent to \begin{array}{l}\require{cancel} 4t^{-4} \left( \dfrac{4t^{-2}}{4t^{-4}}+\dfrac{8t^{-4}}{4t^{-4}} \right) \\\\= 4t^{-4} \left( t^{-2-(-4)}+2t^{-4-(-4)} \right) \\\\= 4t^{-4} \left( t^{-2+4}+2t^{-4+4} \right) \\\\= 4t^{-4} \left( t^{2}+2t^{0} \right) \\\\= 4t^{-4} \left( t^{2}+2(1) \right) \\\\= 4t^{-4} \left( t^{2}+2 \right) .\end{array}
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