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 4 - Polynomials - 4.2 Negative Exponents and Scientific Notations - 4.2 Exercise Set: 76

Answer

$\dfrac{z^{4}}{xy^{6}}$

Work Step by Step

Using the laws of exponents, the given expression, $ (x^3y^{-4}z^{-5})(x^{-4}y^{-2}z^9) $, is equivalent to \begin{array}{l}\require{cancel} x^{3+(-4)}y^{-4+(-2)}z^{-5+9} \\\\= x^{-1}y^{-6}z^{4} \\\\= \dfrac{z^{4}}{x^{1}y^{6}} \\\\= \dfrac{z^{4}}{xy^{6}} .\end{array}
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