Tính
c)\(\frac{4^6.9^5+6^6.120}{8^4.3^{12}-6^{11}}\)
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\(\frac{4^6.9^5+6^6.120}{8^4.3^{12}-6^{11}}=\frac{\left(2^2\right)^6.\left(3^2\right)^5+2^6.3^6.2^3.3.5}{\left(2^3\right)^4.3^{12}-2^{11}.3^{11}}=\frac{2^{12}.3^{10}+2^9.3^7.5}{2^{12}.3^{12}-2^{11}.3^{11}}=\frac{2^9.3^7.\left(2^3.3^3+5\right)}{2^{11}.3^{11}.\left(2.3-1\right)}=\frac{221}{2^2.3^4.5}=\frac{221}{1620}\)
\(C=\dfrac{6^3+3\cdot6^2+3^3}{13}=\dfrac{3^3\cdot8+3^3\cdot4+3^3}{13}=27\)
\(\frac{4^6.9^5+6^9.120}{8^4.3^{12}-6^{11}}=\frac{2^{12}.3^{10}+3^{10}.2^{12}.5}{2^{12}.3^{12}-2^{11}.3^{11}}=\frac{2^{12}.3^{10}.6}{6^{12}-6^{11}}=\frac{2^{12}.3^{10}.6}{6^{11}\left(6-1\right)}=\frac{2^{10}.3^{10}\left(2^2+1\right).6}{6^{11}.5}=\frac{6^{11}.5}{6^{11}.5}=1\)
\(\frac{4^6.9^5+6^9.120}{8^4.3^{12}-6^{11}}.10=\frac{2^{12}.3^{10}+2^9.3^9.120}{2^{12}.3^{12}-2^{11}.3^{11}}.10=\frac{2^{10}.3^{10}\left(2^2+20\right)}{2^{10}.3^{10}\left(6^2-6\right)}.10=\frac{24.10}{30}=8\)