a) $\frac{5^{4}\times20^{4}}{25^{5}\times4^{5}}=\frac{5^{4}\times 4^{4}\times 5^{4}}{5^{10}\times 4^{5}}=\frac{1}{100}$
b)$\frac{4^{3}\times25^{5}\times9^{3}}{8^{2}\times125^{3}\times3^{5}}=\frac{2^{6}\times 5^{10}\times 3^{6}}{2^{6}\times 5^{9}\times 3^{5}}=15$
c) $\frac{6^{3}+3 6^{2}+3^{3}}{-13}=\frac{2^{3}\times 3^{3}+3^{3}\times 2^{2}+3^{3}}{-13}=\frac{3^{3}(2^{3}+2^{2}+1)}{-13}= -3^{3}=-27$