\(\dfrac{7.4^5.3^{11}+2^{15}.9^5}{6^{10}+2^{12}.3^{10}}\)
\(=\dfrac{7.\left(2^2\right)^5.3^{11}+2^{15}.\left(3^2\right)^5}{\left(2.3\right)^{10}+2^{12}.3^{10}}\)
\(=\dfrac{7.2^{10}.3^{11}+2^{15}.3^{10}}{2^{10}.3^{10}+2^{12}.3^{10}}\)
\(=\dfrac{2^{10}.3^{10}\left(7.3+2^5\right)}{2^{10}.3^{10}\left(1+2^2\right)}\)
\(=\dfrac{7.3+2^5}{1+2^2}\)
\(=\dfrac{53}{5}\)