$\text{a)}{0,001}^{-\frac{1}{5}}\cdot {0,001}^{-\frac{2}{15}}={0,001}^{-\frac{1}{5}+\left(-\frac{2}{15}\right)}={0,001}^{-\frac{3}{15}-\frac{2}{15}}={0,001}^{-\frac{5}{15}}={0,001}^{-\frac{1}{3}}={\left(\sqrt[3]{0,001}\right)}^{-1}={0,1}^{-1}={\left(\frac{1}{10}\right)}^{-1}=10$  

$\text{b)}{\left(2^{-\frac{4}{3}}\cdot 8^{\frac{2}{3}}\cdot 4^{\frac{2}{3}}\right)}^{-\frac{3}{2}}={\left[2^{-\frac{4}{3}}\cdot {\left(2^3\right)}^{\frac{2}{3}}\cdot {\left(2^2\right)}^{\frac{2}{3}}\right]}^{-\frac{3}{2}}={\left(2^{-\frac{4}{3}}\cdot 2^2\cdot 2^{\frac{4}{3}}\right)}^{-\frac{3}{2}}={\left(2^{-\frac{4}{3}+2+\frac{4}{3}}\right)}^{-\frac{3}{2}}={\left(2^2\right)}^{-\frac{3}{2}}=2^{-3}={\left(\frac{1}{2}\right)}^3=\frac{1}{8}$  

$\text{c)}{\left({0,008}^{-\frac{2}{3}}\cdot {0,04}^{-3}\right)}^{\frac{3}{8}}={\left[{\left(\sqrt[3]{0,008}\right)}^{-2}\cdot {\left(\frac{4}{100}\right)}^{-3}\right]}^{\frac{3}{8}}={\left[{0,2}^{-2}\cdot {\left(\frac{1}{25}\right)}^{-3}\right]}^{\frac{3}{8}}={\left[{\left(\frac{1}{5}\right)}^{-2}\cdot {25}^3\right]}^{\frac{3}{8}}={\left[5^2\cdot {\left(5^2\right)}^3\right]}^{\frac{3}{8}}={\left(5^2\cdot 5^6\right)}^{\frac{3}{8}}={\left(5^8\right)}^{\frac{3}{8}}=5^3=125$  

$\text{d)}{\left(\frac{3}{20}\right)}^{\frac{1}{4}}\cdot {\left(\frac{5}{12}\right)}^{\frac{1}{4}}={\left(\frac{3}{20}\cdot \frac{5}{12}\right)}^{\frac{1}{4}}={\left(\frac{1}{16}\right)}^{\frac{1}{4}}={\left[{\left(\frac{1}{2}\right)}^4\right]}^{\frac{1}{4}}=\frac{1}{2}$  

$\text{e)}{20}^{\frac{1}{3}}\cdot {2,5}^{-\frac{1}{3}}={20}^{\frac{1}{3}}\cdot {\left(\frac{5}{2}\right)}^{-\frac{1}{3}}={20}^{\frac{1}{3}}\cdot {\left(\frac{2}{5}\right)}^{\frac{1}{3}}={\left(20\cdot \frac{2}{5}\right)}^{\frac{1}{3}}=8^{\frac{1}{3}}=\sqrt[3]{8}=2$  

$\text{f)}{15}^{0,5}\cdot {0,36}^{0,25}={15}^{\frac{1}{2}}\cdot {\left({0,6}^2\right)}^{\frac{1}{4}}={15}^{\frac{1}{2}}\cdot {0,6}^{\frac{1}{2}}={\left(15\cdot 0,6\right)}^{\frac{1}{2}}=9^{\frac{1}{2}}=\sqrt{9}=3$