\(\frac{5\cdot4^{15}\cdot9^9-4\cdot3^{20}\cdot8^9}{5\cdot2^9\cdot6^{14}-7\cdot2^{29}\cdot27^6}\)
\(=\frac{5\cdot\left(2^2\right)^{15}\cdot\left(3^2\right)^9-2^2\cdot3^{20}\cdot\left(2^3\right)^9}{5\cdot2^9\cdot\left(2\cdot3\right)^{14}-7\cdot2^{29}\cdot\left(3^3\right)^6}\)
\(=\frac{5\cdot2^{30}\cdot3^{18}-2^2\cdot3^{20}\cdot2^{27}}{5\cdot2^9\cdot2^{14}\cdot3^{14}-7\cdot2^{29}\cdot3^{18}}\)
\(=\frac{5\cdot2^{30}\cdot3^{18}-2^{29}\cdot3^{20}}{5\cdot2^{23}\cdot3^{14}-7\cdot2^{29}\cdot3^{18}}\)
\(=\frac{2^{29}\cdot3^{18}\cdot\left(5\cdot2\cdot1-1\cdot3^2\right)}{2^{23}\cdot3^{14}\cdot\left(5\cdot1\cdot1-7\cdot2^6\cdot3^4\right)}\)
\(=\frac{2^6\cdot3^4\cdot1}{5-36288}\)
\(=\frac{5184}{-36283}=-\frac{5184}{36283}\)
