166

a)
\sqrt{32}=\sqrt{2^5}=2^{\frac{5}{2}}
b)
\sqrt[5]{16}=\sqrt[5]{2^4}=2^{\frac{4}{5}}
c)
\sqrt{\sqrt[3]{4}}=\sqrt{\sqrt[3]{2^2}}=2^{\frac{2}{6}}=2^{\frac{1}{3}}
d)
\frac{\sqrt[3]{16}}{\sqrt{2}}=\frac{1}{\sqrt{2}}\cdot\sqrt[3]{2^4}=2^{-\frac{1}{2}}\cdot2^{\frac{4}{3}}=2^{-\frac{3}{6}}2^{\frac{8}{6}}=2^{\frac{5}{6}}