$\text{a)}{125}^{\frac{2}{3}}=\sqrt[3]{{125}^2}={\left(\sqrt[3]{125}\right)}^2=5^2=25$     

$\text{b)}{81}^{\frac{3}{4}}=\sqrt[4]{{81}^3}={\left(\sqrt[4]{81}\right)}^3=3^3=27$  

$\text{c)}{\left(\frac{1}{64}\right)}^{-\frac{2}{3}}={64}^{\frac{2}{3}}=\sqrt[3]{{64}^2}={\left(\sqrt[3]{64}\right)}^2=4^2=16$  

$\text{d)}{\left(\frac{8}{27}\right)}^{-\frac{4}{3}}={\left(\frac{27}{8}\right)}^{\frac{4}{3}}=\sqrt[3]{{\left(\frac{27}{8}\right)}^4}={\left(\sqrt[3]{\frac{27}{8}}\right)}^4={\left(\frac{3}{2}\right)}^4=\frac{81}{16}$  

$\text{e)}{9}^{-\frac{3}{2}}={\left(\frac{1}{9}\right)}^{\frac{3}{2}}=\sqrt{{\left(\frac{1}{9}\right)}^3}={\left(\sqrt{\frac{1}{9}}\right)}^3={\left(\frac{1}{3}\right)}^3=\frac{1}{27}$  

$\text{f)}{\left(\frac{81}{625}\right)}^{-0,75}=\frac{{\left(\frac{625}{81}\right)}^3}{4}=\sqrt[4]{{\left(\frac{625}{81}\right)}^3}={\left(\sqrt[4]{\frac{625}{81}}\right)}^3={\left(\frac{5}{3}\right)}^3=\frac{125}{27}$