Answer
a.) $5^{-3} = \frac{1}{125}$
b.) $8^{\frac{2}{3}} = 4$
Work Step by Step
$Express$ $the$ $equation$ $in$ $exponential$ $form:$
a.) $\log_5 (\frac{1}{125}) = -3$
b.) $\log_8 4 = \frac{2}{3}$
Logarithmic form to exponential form: $\log_b a = c \rightarrow b^c = a$
a.) $\log_5 (\frac{1}{125}) = -3$
Plug in 5 for b, $\frac{1}{125}$ for a, and -3 for c
$\log_5 (\frac{1}{125}) = -3 \rightarrow 5^{-3} = \frac{1}{125}$
b.) $\log_8 4 = \frac{2}{3}$
Plug in 8 for b, 4 for a, and $\frac{2}{3}$ for c
$\log_8 4 = \frac{2}{3} \rightarrow 8^{\frac{2}{3}} = 4$