a)
8*\sqrt[3]2=2^3*2^{\frac{1}{3}}=2^{\frac{9}{3}+\frac{1}{3}}=2^{\frac{10}{3}}
\sqrt[3]{3\sqrt3}=3^{\frac{1}{3}}*(\sqrt3)^{\frac{1}{3}}=3^{\frac{1}{3}}*(3^{\frac{1}{3}})^{\frac{1}{3}}=3^{\frac{1}{3}}*3^{\frac{1}{9}}=3^{\frac{3}{9}+\frac{1}{9}}=3^{\frac{4}{9}}
\sqrt{2\sqrt2\sqrt2}=\sqrt{2*2}=2
9*\sqrt[3]3=3^2*3^{\frac{1}{3}}=3^{\frac{6}{3}+\frac{1}{3}}=3^{\frac{7}{3}}