Answer
$16y^{\frac{1}{2}}$
Work Step by Step
$\displaystyle \frac{(2y^{1/5})^{4}}{y^{3/10}}=\qquad$... apply $(ab)^{n}=a^{n}b^{n}$
$=\displaystyle \frac{2^{4}(y^{1/5})^{4}}{y^{3/10}}\qquad$... apply $(a^{m})^{n}=a^{mn}$
$=\displaystyle \frac{16y^{4/5}}{y^{3/10}}\qquad$... apply $\displaystyle \frac{a^{m}}{a^{n}}=a^{m-n}$
...$ \displaystyle \frac{4}{5}-\frac{3}{10}=\frac{8-3}{10}=\frac{5}{10}=\frac{1}{2}$
$=16y^{\frac{1}{2}}$
