Intermediate Algebra (12th Edition)

Published by Pearson
ISBN 10: 0321969359
ISBN 13: 978-0-32196-935-4

Chapter 4 - Section 4.1 - Integer Exponents and Scientific Notation - 4.1 Exercises: 114

Answer

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

Work Step by Step

According to the power rule for exponents, $(a^{m})^{n}=a^{mn}$ (where $m$ and $n$ are integers and $a$ is a real number). Therefore, $(x^{3})^{-4}x^{5}=x^{3\times-4}x^{5}=x^{-12}x^{5}$. According to the product rule for exponents, $a^{m}\times a^{n}=a^{m+n}$. Therefore, $x^{-12}x^{5}=x^{-12+5}=x^{-7}$. According to the negative definition for exponents, $a^{-n}=\frac{1}{a^{n}}$ (where $a\ne0$). Therefore, $x^{-7}=\frac{1}{x^{7}}$.
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