\(\dfrac{5^4}{25^5}.\dfrac{20^4}{4^5}=\dfrac{\left(5.20\right)^4}{\left(25.4\right)^5}=\dfrac{100^4}{100^5}=\dfrac{1}{100}\)
\(\dfrac{5^4}{25^5}\times\dfrac{20^4}{4^5}\)
\(=\dfrac{5^4}{5^{10}}\times\dfrac{5^4\times4^4}{5^5}\)
\(=\dfrac{1}{5^6}\times\dfrac{4^4}{5}\)
\(=\dfrac{4^4}{5^7}\)