Answer
$16y^{\frac{1}{2}}$
Work Step by Step
RECALL:
(1) $a^m \cdot a^n = a^{m+n}$
(2) $\dfrac{a^m}{a^n} = a^{m-n}$
(3) $(ab)^m =a^mb^m$
Use rule (3) above to obtain:
$=\dfrac{2^4(y^{\frac{1}{5}})^4}{y^{\frac{3}{10}}}
\\=\dfrac{2(2)(2)(2)(y^{\frac{1}{5}})^4}{y^{\frac{3}{10}}}
\\=\dfrac{16(y^{\frac{1}{5}})^4}{y^{\frac{3}{10}}}$
Use rule (3) above to obtain:
$=\dfrac{16(y^{\frac{1}{5}(4)})}{y^{\frac{3}{10}}}
\\=\dfrac{16y^{\frac{4}{5}}}{y^{\frac{3}{10}}}$
Use rule (2) above to obtain:
$=16 y^{\frac{4}{5} - \frac{3}{10}}$
Make the fractional exponents similar using their LCD of $10$ to obtain:
$=16 y^{\frac{8}{10} - \frac{3}{10}}
\\=16 y^{\frac{8-3}{10}}
\\=16 y^{\frac{5}{10}}
\\=16y^{\frac{1}{2}}$
