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![](https://rs.olm.vn/images/avt/0.png?1311)
\(\frac{4^6.9^5+6^9.120}{8^4.3^{12}-6^{11}}\) đề là như thế này à hay là sao ???
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
Mình nghĩ đề đúng là :
\(\frac{4^6.9^5+6^9.120}{8^4.3^{12}-6^{11}}\)
\(=\frac{2^{12}.3^{10}+2^9.3^9.3.5.2^3}{2^{12}.3^{12}-2^{11}.3^{11}}\)
\(=\frac{2^{12}.3^{10}+2^{12}.3^{10}.5}{2^{12}.3^{12}-2^{11}.3^{11}}\)
\(=\frac{2^{12}.3^{10}\left(1+5\right)}{2^{11}.3^{11}.\left(2.3-1\right)}\)
\(=\frac{2^{12}.3^{10}.6}{2^{11}.3^{11}.5}\)
\(=\frac{2^{13}.3^{11}}{2^{11}.3^{11}.5}\)
\(=\frac{2^2}{5}\)
\(=\frac{4}{5}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(=\dfrac{2^{12}\cdot3^{10}+2^{12}\cdot3^{10}\cdot5}{-\left(2^{12}\cdot3^{12}+2^{11}\cdot3^{11}\right)}\)
\(=-\dfrac{2^{13}\cdot3^{11}}{2^{11}\cdot3^{11}\left(2\cdot3+1\right)}=\dfrac{-4}{7}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\dfrac{4^6\cdot9^3+6^9\cdot120}{8^4\cdot3^{12}\cdot6^{11}}=\dfrac{2^{12}\cdot3^6+2^9\cdot2^3\cdot3^9\cdot3\cdot5}{2^{12}\cdot3^{23}\cdot2^{11}}\)
\(=\dfrac{2^{12}\cdot3^6+2^{12}\cdot3^{10}\cdot5}{2^{23}\cdot3^{23}}\)
\(=\dfrac{2^{12}\cdot3^6\left(1+3^4\cdot5\right)}{2^{23}\cdot3^{23}}=\dfrac{1}{2^{11}}\cdot\dfrac{1}{3^{17}}\cdot406\)
\(=\dfrac{203}{2^{10}\cdot3^{17}}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\frac{4^6.4^5+6^9.120}{8^4.3^{12}-6^{11}}\)
bạn tự làm nhà, mk tính mệt wá mà mãi ko ra kq