Intermediate Algebra (6th Edition)

Published by Pearson
ISBN 10: 0321785045
ISBN 13: 978-0-32178-504-6

Chapter 5 - Section 5.1 - Exponents and Scientific Notation - Exercise Set: 45

Answer

$\frac{1}{x^{7}}$

Work Step by Step

We are given the expression $\frac{x^{-2}}{x^{5}}$. To simplify, we can use the quotient rule, which holds that $\frac{a^{m}}{a^{n}}=a^{m-n}$ (where a is a nonzero real number, and m and n are integers). Therefore, $\frac{x^{-2}}{x^{5}}=x^{-2-5}=x^{-7}$. To simplify this into a positive exponent, we know that $a^{-n}=\frac{1}{a^{n}}$ (where a is a nonzero real number and n is a positive integer). $x^{-7}=\frac{1}{x^{7}}$
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