a)
3^{\frac{8}{3}}:\sqrt[3]{9}=3^{\frac{8}{3}}:9^{\frac{1}{3}}=3^{\frac{8}{3}}:(3^2)^{\frac{1}{3}}=3^{\frac{8}{3}}:3^{\frac{2}{3}}=3^{\frac{8-2}{3}}=3^{\frac{6}{3}}=3^2
b)
{((\frac{1}{8})^4:32^{-5})^{\frac{1}{2}}=[((\frac{1}{2})^3)^4:(2^5)^{-5}]^{\frac{1}{2}}=[(\frac{1}{2})^{12}:2^{-25}]^{\frac{1}{2}}=(2^{-12-(-25)})^{\frac{1}{2}}=(2^{13)})^{\frac{1}{2}}=2^{\frac{13}{2}}}