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

\(=\frac{2^{12}.3^{10}+2^{12}.3^{10}.5}{-2^{12}.3^{12}-2^{11}.3^{11}}=\frac{2^{12}.3^{10}\left(1+5\right)}{2^{11}.3^{11}\left(-2.3-1\right)}=\frac{2\left(1+5\right)}{3\left(-6-1\right)}=\frac{2.6}{3.\left(-7\right)}=\frac{-12}{21}\)

Bằng -4/7 ghe bạn

\(=-\dfrac{2^{12}\cdot3^{10}+3^9\cdot2^9\cdot2^3\cdot3\cdot5}{2^{12}\cdot3^{12}+2^{11}\cdot3^{11}}\)

\(=-\dfrac{2^{12}\cdot3^{10}+3^{10}\cdot2^{12}\cdot5}{2^{11}\cdot3^{11}\cdot7}\)

\(=-\dfrac{3^{10}\cdot2^{12}\cdot6}{2^{11}\cdot3^{11}\cdot7}=-\dfrac{2}{3}\cdot\dfrac{6}{7}=\dfrac{-12}{21}=-\dfrac{4}{7}\)

\(=\dfrac{2^{12}\cdot3^{10}+2^9\cdot3^9\cdot2^3\cdot3\cdot5}{2^{12}\cdot3^{12}-2^{11}\cdot3^{11}}\)

\(=\dfrac{2^{12}\cdot3^{10}\cdot6}{2^{11}\cdot3^{11}\cdot5}=\dfrac{2}{3}\cdot\dfrac{6}{5}=\dfrac{12}{15}=\dfrac{4}{5}\)

Sửa đề : \(10.\frac{4^6.9^5+6^9.120}{8^4.3^{12}-6^{11}}\)

\(10\cdot\frac{4^6\cdot9^5+6^9\cdot120}{8^4\cdot3^{12}-6^{11}}\)

\(=10\cdot\frac{2^{12}\cdot3^{10}+2\cdot9\cdot3^9\cdot2^3\cdot3\cdot5}{2^{12}.3^{12}-2^{11}.3^{11}}\)

\(=10\cdot\frac{2^{12}\cdot3^{10}\cdot\left(1+5\right)}{2^{11}\cdot3^{11}\cdot\left(2\cdot3-1\right)}\)

\(=10\cdot\frac{2\cdot6}{3\cdot5}=8\)

Bài làm:

\(10.\frac{4^6.9^5+6^9.120}{8^4.3^{12}.6^{11}}\)

\(=\frac{2.5.2^{12}.3^{10}+2^9.3^9.2.5.2^2.3}{2^{12}.3^{12}.2^{11}.3^{11}}\)

\(=\frac{2^{13}.3^{10}.5+2^{12}.3^{10}.5}{2^{23}.3^{23}}\)

\(=\frac{2^{12}.3^{10}.5\left(2+1\right)}{2^{23}.3^{23}}\)

\(=\frac{2^{12}.3^{11}.5}{2^{23}.3^{23}}=\frac{5}{2^{11}.3^{12}}\)

sợ sai

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