Calculus, 10th Edition (Anton)

Published by Wiley
ISBN 10: 0-47064-772-8
ISBN 13: 978-0-47064-772-1

Chapter 6 - Exponential, Logarithmic, And Inverse Trigonometric Functions - 6.1 Exponential And Logarithmic Functions - Exercises Set 6.1 - Page 418: 1

Answer

$$\left( a \right)4,\,\,\,\,\left( b \right)4,\,\,\,\left( c \right)\frac{1}{4}$$

Work Step by Step

$$\eqalign{ & \left( {\bf{a}} \right)\,\,\,\, - {8^{2/3}} \cr & {\text{Use the property }}{\left( {{a^m}} \right)^n} = {a^{mn}} \cr & = - {\left( {{8^{1/3}}} \right)^2} \cr & {\text{Use the property }}{a^{m/n}} = \root n \of {{a^m}} \cr & = - {\left( {\root 3 \of 8 } \right)^2} \cr & = - {\left( 2 \right)^2} \cr & {\text{simplify}} \cr & = - 4 \cr & \cr & \left( {\bf{b}} \right)\,\,\,\,{\left( { - 8} \right)^{2/3}} \cr & {\text{Use the property }}{\left( {{a^m}} \right)^n} = {a^{mn}} \cr & = {\left( { - {8^{1/3}}} \right)^2} \cr & {\text{Use the property }}{a^{m/n}} = \root n \of {{a^m}} \cr & = {\left( {\root 3 \of { - 8} } \right)^2} \cr & = {\left( { - 2} \right)^2} \cr & {\text{simplify}} \cr & = 4 \cr & \cr & \left( {\bf{c}} \right)\,\,\,\,{8^{ - 2/3}} \cr & {\text{Use the property }}{\left( {{a^m}} \right)^n} = {a^{mn}} \cr & = {\left( {{8^{1/3}}} \right)^{ - 2}} \cr & {\text{Use the property }}{a^{m/n}} = \root n \of {{a^m}} \cr & = {\left( {\root 3 \of 8 } \right)^{ - 2}} \cr & = {\left( 2 \right)^{ - 2}} \cr & {\text{Use the property }}{a^{ - n}} = \frac{1}{{{a^n}}} \cr & = \frac{1}{{{{\left( 2 \right)}^2}}} \cr & {\text{simplify}} \cr & = \frac{1}{4} \cr} $$
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