22) \(\dfrac{5^4\cdot20^4}{25^5\cdot4^5}\)
\(=\dfrac{5^4\cdot5^4\cdot4^4}{\left(5^2\right)^5\cdot4^5}\)
\(=\dfrac{5^8\cdot4^4}{5^{10}\cdot4^5}\)
\(=\dfrac{1\cdot1}{5^2\cdot4}\)
\(=\dfrac{1}{100}\)
23) \(\dfrac{3^7\cdot9^3}{81\cdot27^2}\)
\(=\dfrac{3^7\cdot\left(3^2\right)^3}{3^4\cdot\left(3^3\right)^2}\)
\(=\dfrac{3^7\cdot3^6}{3^4\cdot3^6}\)
\(=\dfrac{3^3\cdot1}{1\cdot1}\)
\(=27\)
24) \(\dfrac{45^{10}\cdot5^{20}}{75^{15}}\)
\(=\dfrac{5^{10}\cdot3^{20}\cdot5^{20}}{5^{30}\cdot3^{15}}\)
\(=\dfrac{5^{30}\cdot3^{20}}{5^{30}\cdot3^{15}}\)
\(=\dfrac{1\cdot3^5}{1\cdot1}\)
\(=243\)