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: 97



Work Step by Step

We are given the expression $\frac{x^{3t}\times x^{4t-1}}{x^{t}}$. To simplify the numerator we can use the product rule, which holds that $a^{m}\times a^{n}=a^{m+n}$ (where a is a real number, and m and n are positive integers). $\frac{x^{3t}\times x^{4t-1}}{x^{t}}=\frac{x^{3t+4t-1}}{x^{t}}=\frac{x^{7t-1}}{x^{t}}$ Next, we can use the quotient rule to simplify, which holds that $\frac{a^{m}}{a^{n}}=a^{m-n}$ (where a is a nonzero real number, and m and n are integers). $\frac{x^{7t-1}}{x^{t}}=x^{7t-1-t}=x^{6t-1}$
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