${20}^4={\left(4\cdot 5\right)}^4={\left(2^2\cdot 5\right)}^4={\left(2^2\right)}^4\cdot 5^4=2^{2\cdot 4}\cdot 5^4=2^8\cdot 5^4$  

${15}^3={\left(3\cdot 5\right)}^3=3^3\cdot 5^3$  

${12}^3={\left(3\cdot 4\right)}^3={\left(3\cdot 2^2\right)}^3=3^3\cdot {\left(2^2\right)}^3=3^3\cdot 2^{2\cdot 3}=3^3\cdot 2^6$  

$5^4$  

Obliczamy teraz ile wynosi wartość wyrażenia. 

$\frac{{20}^4\cdot {15}^3}{{12}^3\cdot 5^4}=\frac{2^8\cdot 5^4\cdot {\sout{3^3}}^1\cdot 5^3}{{\sout{3^3}}_1\cdot 2^6\cdot 5^4}=\frac{2^8\cdot {\sout{5^4}}^1\cdot 5^3}{2^6\cdot {\sout{5^4}}_1}=\frac{2^8\cdot 5^3}{2^6}=$    

$=\frac{2^8}{2^6}\cdot 5^3=2^{8-6}\cdot 5^3=2^2\cdot 5^3=4\cdot 125=500$  

Poprawna odpowiedź: C. 500