Elementary Algebra

Published by Cengage Learning
ISBN 10: 1285194055
ISBN 13: 978-1-28519-405-9

Chapter 5 - Exponents and Polynomials - 5.6 - Integral Exponents and Scientific Notation - Problem Set 5.6: 84

Answer

$\dfrac{1}{5x^{3}}$

Work Step by Step

Using the laws of exponents, the given expression, $ \left( \dfrac{35x^{2}}{7x^{-1}} \right)^{-1} ,$ simplifies to \begin{array}{l}\require{cancel} \left( (35\div7)x^{2-(-1)} \right)^{-1} \\\\= \left( 5x^{2+1} \right)^{-1} \\\\= \left( 5x^{3} \right)^{-1} \\\\= \dfrac{1}{\left( 5x^{3} \right)^{1}} \\\\= \dfrac{1}{5x^{3}} .\end{array}
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