$a)6^3\cdot {\left(\frac{1}{3}\right)}^3={\left({\sout{6}}^2\cdot \frac{1}{{\sout{3}}^1}\right)}^3=2^3=8$

$b){0,2}^4\cdot {10}^4={\left(0,2\cdot 10\right)}^4=2^4=16$

$c)7^4\cdot {\left(\frac{2}{7}\right)}^4={\left({\sout{7}}^1\cdot \frac{2}{{\sout{7}}^1}\right)}^4=2^4=16$

$d){0,1}^{10}\cdot {10}^{10}={\left(0,1\cdot 10\right)}^{10}=1^{10}=1$

$e)4^5\cdot {\left(\frac{1}{2}\right)}^5={\left({\sout{4}}^2\cdot \frac{1}{{\sout{2}}^1}\right)}^5=2^5=32$

$f){25}^{-1}\cdot {0,004}^{-1}={\left(25\cdot 0,004\right)}^{-1}={\left(25\cdot \frac{4}{1000}\right)}^{-1}={\left(\frac{100}{1000}\right)}^{-1}={\left(\frac{1}{10}\right)}^{-1}=10$

$g){\left(-2\right)}^6\cdot 5^6\cdot {\left(-0,1\right)}^6={\left(-2\cdot 5\cdot \left(-0,1\right)\right)}^6={\left(-10\cdot \left(-0,1\right)\right)}^6=1^6=1$

$h){\left(\frac{3}{4}\right)}^{-2}\cdot {\left(\frac{2}{3}\right)}^{-2}\cdot 4^{-2}={\left(\frac{{\sout{3}}^1}{{\sout{4}}^1}\cdot \frac{2}{{\sout{3}}^1}\cdot {\sout{4}}^1\right)}^{-2}=2^{-2}={\left(\frac{1}{2}\right)}^2=\frac{1}{4}$