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: 75

Answer

$\frac{1}{x^{9}y^{4}}$

Work Step by Step

We are given the expression $\frac{x^{-7}y^{-2}}{x^{2}y^{2}}$. 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). $\frac{x^{-7}y^{-2}}{x^{2}y^{2}}=x^{-7-2}\times y^{-2-2}=x^{-9}\times y^{-4}$ To simplify this into only positive exponents, we know that $a^{-n}=\frac{1}{a^{n}}$ (where a is a nonzero real number and n is a positive integer). $x^{-9}\times y^{-4}=\frac{1}{x^{9}y^{4}}$
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.