\(\frac{45^{10}.5^{20}}{75^5}\)
\(=\frac{\left(3^2.5\right)^{10}.5^{20}}{\left(5^2.3\right)^5}\)
\(=\frac{3^{20}.5^{10}.5^{20}}{5^{10}.3^5}\)
\(=3^{15}.5^{20}\)
\(\frac{45^{10}.5^{20}}{75^5}=\frac{9^{10}.5^{10}.5^{20}}{25^5.3^5}=\frac{3^{20}.5^{10}.5^{20}}{5^{10}.3^5}=\frac{3^{20}.5^{30}}{5^{10}.3^5}=3^{15}.5^{20}\)