$a)\left(6^4:{\left(0.4\right)}^4\right):5^4={\left(6:0,4\right)}^4:5^4={\left(6:\frac{2}{5}\right)}^4:5^4={\left({\sout{6}}^3\cdot \frac{5}{{\sout{2}}^2}\right)}^4:5^4={15}^4:5^4={\left(15:5\right)}^4=3^4=81$  

$b)\left({\left(2,25\right)}^5\cdot {\left(-4\right)}^5\right):3^5={\left(2,25\cdot \left(-4\right)\right)}^5:3^5={\left(-9\right)}^5:3^5={\left(-9:3\right)}^5={\left(-3\right)}^5=-243$  

$c)\left({\left(0,25\right)}^4:{\left(1\frac{2}{3}\right)}^4\right)\cdot 2^4={\left(0,25:1\frac{2}{3}\right)}^4\cdot 2^4={\left(\frac{1}{4}:1\frac{2}{3}\right)}^4\cdot 2^4={\left(\frac{1}{4}:\frac{5}{3}\right)}^4\cdot 2^4=$  

${\left(\frac{1}{4}\cdot \frac{3}{5}\right)}^4\cdot 2^4={\left(\frac{3}{20}\right)}^4:2^4={\left(\frac{3}{{\sout{20}}^{10}}\cdot {\sout{2}}^1\right)}^4={\left(\frac{3}{10}\right)}^4=\frac{81}{10000}$

  $d){\left(1,2\right)}^5:\left({\left(2,4\right)}^5:{\left(0,4\right)}^5\right)={\left(1,2\right)}^5:{\left(2,4:0,4\right)}^5={\left(1,2\right)}^5:6^5={\left(1,2:6\right)}^5={\left(0,2\right)}^5={\left(\frac{1}{5}\right)}^5=\frac{1}{3125}$  

$e)\left({\left(\frac{2}{3}\right)}^3\cdot {\left(2,4\right)}^3\right):\left({\left(2\frac{2}{3}\right)}^3\cdot {\left(1,5\right)}^3\right)={\left(\frac{2}{3}\cdot 2,4\right)}^3:{\left(2\frac{2}{3}\cdot 1,5\right)}^3={\left(\frac{{\sout{2}}^1}{{\sout{3}}^1}\cdot \frac{{\sout{24}}^8}{{\sout{10}}^5}\right)}^3:{\left(\frac{8}{3}\cdot 1\frac{1}{2}\right)}^3=$  

${\left(\frac{8}{5}\right)}^3:{\left(\frac{{\sout{8}}^4}{{\sout{3}}^1}\cdot \frac{{\sout{3}}^1}{{\sout{2}}^1}\right)}^3={\left(\frac{8}{5}\right)}^3:4^3={\left(\frac{8}{5}:4\right)}^3={\left(\frac{{\sout{8}}^2}{5}\cdot \frac{1}{{\sout{4}}^1}\right)}^3={\left(\frac{2}{5}\right)}^3=\frac{8}{125}$