Intermediate Algebra (6th Edition)

Published by Pearson

Chapter 5 - Section 5.2 - More Work with Exponents and Scientific Notation - Exercise Set: 3

Answer

$\frac{1}{x^{36}}$

Work Step by Step

We are given the expression $(x^{4})^{-9}$. To simplify, we can use the power rule, which holds that $(a^{m})^{n}=a^{m\times n}$ (where a is a real number, and m and n are integers). $(x^{4})^{-9}=x^{4\times-9}=x^{-36}$ 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). Therefore, $x^{-36}=\frac{1}{x^{36}}$

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