College Algebra 7th Edition

Published by Brooks Cole
ISBN 10: 1305115546
ISBN 13: 978-1-30511-554-5

Chapter P, Prerequisites - Section P.3 - Integer Exponents and Scientific Notation - P.3 Exercises: 9

Answer

No, $(\frac{2}{3})^{-2}$ is not equal to $3^{4}$. Yes, there is difference between $(-5)^{4}$ and $-5^{4}$.

Work Step by Step

A. $(\frac{2}{3})^{-2}$ = $(\frac{3}{2})^{2}$ = $\frac{3\times3}{2\times2}$ = $\frac{9}{4}$ which $\ne$ $\frac{3}{4}$ B. Here, $(-5)^{4}$ = $(-5)\times(-5)\times(-5)\times(-5)$ = 625 $-5^{4}$ = -($5\times5\times5\times5$) = -625 and 625 $\ne$ -625, so there is difference between $(-5)^{4}$ and$-5^{4}$.
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