a)
\sqrt[5]{7}=7^{\frac{1}{5}}
b)
\sqrt[3]{7^2}=7^{\frac{2}{3}}
c)
\frac{1}{\sqrt[3]{7}}=(\sqrt[3]{7})^{-1}=(7^{\frac{1}{3}})^{-1}=7^{-\frac{1}{3}}
d)
\frac{1}{\sqrt[5]{7^3}}=(\sqrt[5]{7^3})^{-1}=(7^{\frac{3}{5}})^{-1}=7^{-\frac{3}{5}}
e)
7*\sqrt[5]{7} = 7^1*7^{\frac{1}{5}}=7^{\frac{6}{5}}