\(\dfrac{5\cdot4^{15}\cdot9^9-4\cdot3^{20}\cdot8^9}{5\cdot2^9\cdot6^{10}-7\cdot2^{29}\cdot27^6}\)
\(=\dfrac{5\cdot2^{30}\cdot3^{18}-2^{29}\cdot3^{20}}{5\cdot2^{19}\cdot3^{10}-7\cdot2^{29}\cdot3^{18}}\)
\(=\dfrac{2^{29}\cdot3^{18}\cdot\left(5\cdot2-3^2\right)}{2^{19}\cdot3^{10}\cdot\left(5-7\cdot2^{10}\cdot3^8\right)}\)
\(=\dfrac{2^{10}\cdot3^8}{5-7\cdot2^{10}\cdot3^8}\)
