$a)8^{\frac{4}{3}}={\left(\sqrt[3]{8}\right)}^4=2^4=16$

$b){32}^{\frac{3}{5}}={\left(\sqrt[5]{32}\right)}^3=2^3=8$

$c){81}^{1,5}={81}^{\frac{3}{2}}={\sqrt{81}}^3=9^3=729$

$d)4^{-\frac{3}{2}}={\left(\frac{1}{4}\right)}^{\frac{3}{2}}={\sqrt{\frac{1}{4}}}^3={\left(\frac{1}{2}\right)}^3=\frac{1}{8}$

$e){125}^{-\frac{2}{3}}={\left(\frac{1}{125}\right)}^{\frac{2}{3}}={\sqrt[3]{\frac{1}{125}}}^2={\left(\frac{1}{5}\right)}^2=\frac{1}{25}$

$f){\left(\frac{1}{81}\right)}^{-\frac{3}{4}}={81}^{\frac{3}{4}}={\sqrt[4]{81}}^3=3^3=27$

$g){\left(\frac{1}{4}\right)}^{-2,5}=4^{2,5}=4^{\frac{5}{2}}={\sqrt{4}}^5=2^5=32$

$h){\left(\frac{8}{27}\right)}^{-\frac{2}{3}}={\left(\frac{27}{8}\right)}^{\frac{2}{3}}={\sqrt[3]{\frac{27}{8}}}^2={\left(\frac{3}{2}\right)}^2=\frac{9}{4}$