\frac{16^{\frac{1}{2}}*\sqrt[4]2*\sqrt[3]8}{\sqrt2*\sqrt[3]4}=\frac{(2^4)^{\frac{1}{2}}*2^{\frac{1}{2}}*2}{2^{\frac{1}{2}}*2^{\frac{2}{3}}}
=\frac{2^2*2^{\frac{1}{4}}*2}{2^{\frac{3+4}{6}}}=\frac{2^{\frac{13}{4}}}{2^{\frac{7}{6}}}=2^{\frac{13}{4}-\frac{7}{6}}=2^{\frac{39-14}{12}}=2^{\frac{25}{12}}