$\text{a)}{8}^4\cdot {27}^3\cdot 6^{-11}={\left(2^3\right)}^4\cdot {\left(3^3\right)}^3\cdot {\left(2\cdot 3\right)}^{-11}=2^{12}\cdot 3^9\cdot 2^{-11}\cdot 3^{-11}=2\cdot 3^{-2}=$  

$=2\cdot \frac{1}{9}=\frac{2}{9}$   

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$\text{b)}\frac{{12}^6\cdot 4^{-4}}{{18}^{-1}\cdot 6^7}=\frac{{\left(3\cdot 4\right)}^6\cdot 4^{-4}}{{\left(3\cdot 6\right)}^{-1}\cdot 6^7}=\frac{3^6\cdot 4^6\cdot 4^{-4}}{3^{-1}\cdot 6^{-1}\cdot 6^7}=\frac{3^6\cdot 4^2}{3^{-1}\cdot 6^6}=\frac{3^6\cdot {\left(2^2\right)}^2}{3^{-1}\cdot {\left(2\cdot 3\right)}^6}=$  

$=\frac{3^6\cdot 2^4}{3^{-1}\cdot 2^6\cdot 3^6}=\frac{3^6\cdot 2^4}{2^6\cdot 3^5}=\frac{3}{2^2}=\frac{3}{4}$  

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$\text{c)}{0,5}^{-5}\cdot {10}^6:{20}^5={\left(\frac{1}{2}\right)}^{-5}\cdot {\left(2\cdot 5\right)}^6:{\left(2^2\cdot 5\right)}^5=2^5\cdot 2^6\cdot 5^6:\left(2^{10}\cdot 5^5\right)=$  

$=2^{11}\cdot 5^6:\left(2^{10}\cdot 5^5\right)=2^{11-10}\cdot 5^{6-5}=2\cdot 5=10$  

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$\text{d)}\frac{400\cdot {16}^{-3}-80\cdot {0,25}^6}{10\cdot 2^9}=\frac{2^2\cdot {10}^2\cdot {\left(2^4\right)}^{-3}-2^3\cdot 10\cdot {\left(\frac{1}{4}\right)}^6}{10\cdot 2^9}=$  

$=\frac{2^2\cdot {10}^2\cdot 2^{-12}-2^3\cdot 10\cdot {\left(2^{-2}\right)}^6}{10\cdot 2^9}=\frac{2^{-10}\cdot {10}^2-2^3\cdot 10\cdot 2^{-12}}{10\cdot 2^9}=$  

$=\frac{2^{-10}\cdot {10}^2-2^{-9}\cdot 10}{10\cdot 2^9}=\frac{2^{-10}\cdot 10-2^{-9}}{2^9}=2^{-19}\cdot 10-2^{-18}=$  

$=2^{-18}\cdot 2^{-1}\cdot 10-2^{-18}\cdot 1=2^{-18}\cdot \left(2^{-1}\cdot 10-1\right)=2^{-18}\cdot \left(\frac{1}{2}\cdot 10-1\right)=$  

$=2^{-18}\cdot 4=2^{-18}\cdot 2^2=2^{-16}$  

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$\text{e)}\left({0,64}^{-6}:{2,5}^{10}\right)\cdot {0,25}^{-8}=\left({\left(\frac{64}{100}\right)}^{-6}:{\left(2\frac{1}{2}\right)}^{10}\right)\cdot {\left(\frac{1}{4}\right)}^{-8}=$  

$=\left({\left(\frac{16}{25}\right)}^{-6}:{\left(\frac{5}{2}\right)}^{10}\right)\cdot {\left(2^{-2}\right)}^{-8}=\left({\left(\frac{2^4}{5^2}\right)}^{-6}\cdot {\left(\frac{2}{5}\right)}^{10}\right)\cdot 2^{16}=$  

$=\frac{2^{-24}}{5^{-12}}\cdot \frac{2^{10}}{5^{10}}\cdot 2^{16}=\frac{2^{-24+10+16}}{5^{-12+10}}=\frac{2^2}{5^{-2}}=\frac{4}{\frac{1}{25}}=4:\frac{1}{25}=4\cdot 25=100$  

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$\text{f)}{15}^{-2}\cdot {\left(\frac{19}{20}\right)}^{-3}\cdot {\left(\frac{4}{57}\right)}^{-3}={15}^{-2}\cdot {\left(\frac{{\sout{19}}^1}{{\sout{20}}^5}\cdot \frac{{\sout{4}}^1}{{\sout{57}}^3}\right)}^{-3}={15}^{-2}\cdot {\left(\frac{1}{15}\right)}^{-3}=$  

$={15}^{-2}\cdot {15}^3=15$