Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

Published by Pearson
ISBN 10: 0-32184-874-8
ISBN 13: 978-0-32184-874-1

Chapter 10 - Exponents and Radicals - 10.2 Rational Numbers as Exponents - 10.2 Exercise Set: 74

Answer

$\dfrac{1}{2.7^{\frac{3}{4}}}$

Work Step by Step

Using the laws of exponents, the given expression, $ \dfrac{2.7^{-11/12}}{2.7^{-1/6}} ,$ simplifies to \begin{array}{l}\require{cancel} 2.7^{-\frac{11}{12}-\left( -\frac{1}{6} \right)} \\\\= 2.7^{-\frac{11}{12}+\frac{1}{6}} \\\\= 2.7^{-\frac{11}{12}+\frac{2}{12}} \\\\= 2.7^{-\frac{9}{12}} \\\\= 2.7^{-\frac{3}{4}} \\\\= \dfrac{1}{2.7^{\frac{3}{4}}} .\end{array}
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