\(\frac{4^6.9^5+6^9.120}{8^4.3^{12}-6^{11}}=\frac{\left(2^2\right)^6.\left(3^2\right)^5+\left(2.3\right)^9.2^3.3.5}{\left(2^3\right)^4.3^{12}-\left(2.3\right)^{11}}\)
\(=\frac{2^{12}.3^{10}+2^{12}.3^{10}.5}{2^{12}.3^{12}-2^{11}.3^{11}}\)
\(=\frac{2^{12}.3^{10}}{2^{11}.3^{11}}.\frac{1+5}{2.3-1}\)
\(=\frac{2^{12}.3^{10}}{2^{11}.3^{11}}.\frac{6}{5}\)
\(=\frac{2}{3}.\frac{6}{5}\)
\(=\frac{4}{5}\)
\(=\frac{\left(2^2\right)^6.\left(3^2\right)^5+\left(2.3\right)^9.8.3.5}{\left(2^3\right)^4.3^{12}+\left(2.3+1\right)}=\frac{2^{12}.3^{10}+2^9.3^9.2^3.3.5}{2^{12}.3^{12}+2^{11}.3^{11}}=\frac{2^{12}.3^{10}.\left(1+5\right)}{2^{11}.3^{11}.\left(2.3+1\right)} \)
\(\frac{2.3.6}{7}=\frac{36}{7}\)
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