\(\frac{4^6.9^5+6^9.120}{8^4.3^{12}-6^{11}}\)
\(=\frac{2^{12}.3^{10}+2^9.3^9.2^3.3.5}{2^{12}.3^{12}-2^{11}.3^{11}}\)
\(=\frac{2^{12}.3^{10}+2^{12}.3^{10}.5}{2^{11}.3^{11}.\left(2.3-1\right)}\)
\(=\frac{2^{12}.3^{10}.\left(1+5\right)}{2^{11}.3^{11}.5}\)
\(=\frac{2.6}{3.5}=\frac{4}{5}\)
\(\frac{4^6.9^5+6^9.120}{8^4.3^{12}-6^{11}}\)
\(=\frac{2^{12}.3^{10}+2^9.3^9.2^3.3.5}{2^{12}.3^{12}-6^{11}}\)
\(=\frac{2^{12}.3^{10}+2^{12}.3^{10}.5}{6^{12}-6^{11}}\)
\(=\frac{2^{12}.3^{10}\left(1+5\right)}{6^{11}.6-6^{11}}\)
\(=\frac{\left(2.3\right)^{10}.2^2.6}{6^{11}\left(6-1\right)}\)
\(=\frac{6^{10}.6.2^2}{6^{11}.5}=\frac{6^{11}.2^2}{6^{11}.5}=\frac{2^2}{5}=\frac{4}{5}\)
