Intermediate Algebra (12th Edition)

Published by Pearson
ISBN 10: 0321969359
ISBN 13: 978-0-32196-935-4

Chapter 5 - Section 5.1 - Greatest Common Factors and Factoring by Grouping - 5.1 Exercises: 73


$m^{-5} \left( 3+m^{2} \right)$

Work Step by Step

$\bf{\text{Solution Outline:}}$ Factor the variable with the lesser exponent in the given expression, $ 3m^{-5}+m^{-3} .$ Then, divide the given expression and the variable with the lesser exponent. $\bf{\text{Solution Details:}}$ Factoring $ m^{-5} $ (the variable with the lesser exponent), the expression above is equivalent to \begin{array}{l}\require{cancel} m^{-5} \left( \dfrac{3m^{-5}}{m^{-5}}+\dfrac{m^{-3}}{m^{-5}} \right) .\end{array} Using the Quotient Rule of the laws of exponents which states that $\dfrac{x^m}{x^n}=x^{m-n},$ the expression above simplifies to \begin{array}{l}\require{cancel} m^{-5} \left( 3m^{-5-(-5)}+m^{-3-(-5)} \right) \\\\= m^{-5} \left( 3m^{-5+5}+m^{-3+5} \right) \\\\= m^{-5} \left( 3m^{0}+m^{2} \right) \\\\= m^{-5} \left( 3(1)+m^{2} \right) \\\\= m^{-5} \left( 3+m^{2} \right) .\end{array}
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