Answer
$= \frac{1}{5}log_2(x) + \frac{4}{5}log_2(y) - \frac{4}{5}$
Work Step by Step
$= log_2(\sqrt[5] {\frac{xy^{4}}{16}})$
$=log_2(\frac{xy^{4}}{16})^{\frac{1}{5}}$
$=\frac{1}{5}log_2(\frac{xy^{4}}{16})$
$= \frac{1}{5}log_2(xy^{4}) - \frac{1}{5}log_2(16)$
$=\frac{1}{5}log_2(x) + \frac{1}{5}log_2(y^{4}) - \frac{1}{5}log_2(2^{4})$
$= \frac{1}{5}log_2(x) + \frac{4}{5}log_2(y) - \frac{4}{5}log_2(2)$
$= \frac{1}{5}log_2(x) + \frac{4}{5}log_2(y) - \frac{4}{5}$