\(\frac{4^6.9^5+6^9.120}{\left(-8\right)^4.3^{12}-6^{11}}=\frac{2^{12}.3^{10}+2^9.3^9.2^3.3.5}{8^4.3^{12}-6^{11}}=\frac{2^{12}.3^{10}+2^{12}.3^{10}.5}{2^{12}.3^{12}-6^{11}}\)
\(=\frac{\left(2^{12}.3^{10}\right)\left(1+5\right)}{6^{12}-6^{11}}=\frac{6\left(2^{12}.3^{10}\right)}{6^{11}\left(6-1\right)}=\frac{2^{10}.3^{10}.2^2}{6^{10}.5}=\frac{6^{10}.4}{6^{10}.5}=\frac{4}{5}\)
\(\text{Ta có:}\)
\(\frac{4^6.9^5+6^9.120}{\left(-8\right)^4.3^{12}-6^{11}}\)\(=\frac{2^{12}.3^{10}+2^9.3^9.2^3.3.5}{8^4.3^{12}-6^{11}}\)
\(=\frac{2^{12}.3^{10}+2^{12}.3^{10}.5}{2^{12}.3^{12}-6^{11}}\)
\(=\frac{\left(2^{12}.3^{10}\right)\left(1+5\right)}{6^{12}-6^{11}}\)
\(=\frac{6\left(2^{12}.3^{10}\right)}{6^{11}\left(6-1\right)}\)
\(=\frac{2^{10}.3^{10}.2^2}{6^{10}.5}=\frac{6^{10}.4}{6^{10}.5}=\frac{4}{5}\)