Trả lời:
\(\frac{4^6.9^9+6^9.102}{8^4.3^{12}-6^{11}}=\frac{\left(2^2\right)^6.\left(3^2\right)^6+\left(2.3\right)^9.2.3.17}{\left(2^3\right)^4.3^{12}-\left(2.3\right)^{11}}=\frac{2^{12}.3^{12}+2^9.3^9.2.3.17}{2^{12}.3^{12}-2^{11}.3^{11}}\)
\(=\frac{2^{12}.3^{12}+2^{10}.3^{10}.17}{2^{12}.3^{12}-2^{11}.3^{11}}=\frac{2^{10}.3^{10}.\left(2^2.3^2+17\right)}{2^{10}.3^{10}.\left(2^2.3^2-2.3\right)}=\frac{2^2.3^2+17}{2^2.3^2-2.3}=\frac{53}{30}\)