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 - Page 262: 76



Work Step by Step

We are given the expression $\frac{a^{-5}b^{7}}{a^{-2}b^{-3}}$. 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). $\frac{a^{-5}b^{7}}{a^{-2}b^{-3}}=a^{-5-(-2)}\times b^{7-(-3)}=a^{-3}\times b^{10}$ 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). $a^{-3}\times b^{10}=\frac{b^{10}}{a^{3}}$
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