College Algebra (11th Edition)

Published by Pearson
ISBN 10: 0321671791
ISBN 13: 978-0-32167-179-0

Chapter R - Section R.6 - Rational Exponents - R.6 Exercises - Page 55: 1

Answer

$\begin{array}{ c c } a) & \mathrm{Choice\ }\mathbf{B}\\ b) & \mathrm{Choice\ }\mathbf{D}\\ c) & \mathrm{Choice\ }\mathbf{B}\\ d) & \mathrm{Choice\ }\mathbf{D} \end{array}$

Work Step by Step

$\begin{array}{|c|l|} \hline a) & \begin{array}{l} \mathrm{Recall\ the\ exponent\ rule\ } a^{-b} \ =\ \dfrac{1}{a^{b}} .\ \\ \mathrm{Apply\ the\ rule\ for\ case\ a) :}\\ =\dfrac{1}{4^{2}} =\dfrac{1}{( 4)( 4)} =\dfrac{1}{16} \ \mathrm{which\ matches\ Choice\ }\mathbf{B} .\ \end{array}\\ & \\ \hline b) & \begin{array}{l} \mathrm{For\ case\ b}) :\\ =-\dfrac{1}{4^{2}} =-\dfrac{1}{( 4)( 4)} =-\dfrac{1}{16} \ \mathrm{which\ matches\ Choice\ }\mathbf{D} . \end{array}\\ & \\ \hline c) & \begin{array}{l} \mathrm{For\ case\ c}) :\ \\ =\dfrac{1}{( -4)^{2}} =\dfrac{1}{( -4)( -4)} =\dfrac{1}{16} \ \mathrm{which\ matches\ Choice} \ \mathbf{B} . \end{array}\\ & \\ \hline d) & \begin{array}{l} \mathrm{For\ case\ d) :}\\ =-\dfrac{1}{( -4)^{2}} =-\dfrac{1}{( -4)( -4)} =-\dfrac{1}{16} \ \mathrm{which\ matches\ Choice} \ \mathbf{D} \end{array}\\ \hline \end{array}$
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