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: 87

Answer

$-\frac{64m^{6}}{t^{3}}$

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, $(\frac{-4m^{2}}{t})^{3}=(\frac{-1\times4\times m^{2}}{t})^{3}=\frac{(-1)^{1\times3}4^{1\times3}m^{2\times3}}{t^{1\times3}}=\frac{(-1)^{3}4^{3}m^{6}}{t^{3}}=\frac{-1\times64\times m^{6}}{t^{3}}=\frac{-64m^{6}}{t^{3}}=-\frac{64m^{6}}{t^{3}}$.
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