\(\frac{4^{10}.20^{10}}{75^{15}}\)
\(=\frac{1125^{10}}{75^5.75^{10}}\)
\(=\frac{1125^{10}}{75}\)
\(=\frac{1}{75^5}\)
\(=\frac{15^{10}}{75^5}\)
\(=\frac{15^5.15^5}{75^5}\)
\(=\frac{15^5}{75}.15^5\)
\(=\frac{1}{3}^5.15^5\)
\(=\frac{1}{3}.15^5\)
\(=^{5^5}\)
\(=3125\)