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: 85

Answer

$-216x^{6}$

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, $(-6x^{2})^{3}=(-1\times6\times x^{2})^{3}=(-1)^{1\times3}\times6^{1\times3}\times x^{2\times3}=(-1)^{3}\times6^{3}\times x^{6}=-1\times216\times x^{6}=-216x^{6}$.
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