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\(=\dfrac{2^{12}\cdot3^{10}+2^{12}\cdot3^{10}\cdot5}{2^{12}\cdot3^{12}+2^{11}\cdot3^{11}}=\dfrac{2^{13}\cdot3^{11}}{2^{11}\cdot3^{11}\cdot7}=\dfrac{4}{7}\)
\(\frac{4^6.9^5+6^9.120}{8^4.3^{12}-6^{11}}=\frac{241864704+1209323520}{2176782336-362797056}=\frac{4}{5}\)
\(\frac{4^6.9^5+6^9.120}{8^4.3^{12}-6^{11}}\)= \(\frac{4096.59049+10077696.120}{4096.531441-362797056}\)= \(\frac{241864704+1209323520}{2176782336-362797056}\)= \(\frac{1451188224}{1813985280}\)
\(A=\)\(\frac{4^6.9^5+6^9.120}{6^{11}+8^4.3^{12}}\)
\(A=\frac{2^{12}.3^{10}+6^9.6.2^2.5}{6^{11}+2^{12}.3^{12}}\)
\(A=\frac{2^{12}.3^{10}+6^{10}.2^2.5}{6^{11}+2^{12}.3^{12}}\)
\(A=\frac{2^{12}.3^{10}+2^{10}.3^{10}.2^2.5}{\left(2.3\right)^{11}+2^{12}.3^{12}}\)
\(A=\frac{2^{12}.3^{10}+2^{12}.3^{10}.5}{2^{11}.3^{11}+2^{12}.3^{12}}\)
\(A=\frac{2^{12}.3^{10}.\left(1+5\right)}{2^{11}.3^{11}.\left(1+2.3\right)}\)
\(A=\frac{2^{12}.3^{10}.6}{2^{11}.3^{11}.7}\)
\(A=\frac{2^{12}.3^{10}.2.3}{2^{11}.3^{11}.7}\)
\(A=\frac{2^{13}.3^{11}}{2^{11}.3^{11}.7}\)
\(A=\frac{2^2}{7}\)\(=\frac{4}{7}\)
Em kiểm tra lại đề nhé!
Nếu đề đúng:
\(10\cdot\frac{4^6\cdot9^5+69\cdot120}{8^4\cdot3^{12}-6^{11}}\)
\(=10\cdot\frac{\left(2^2\right)^6\cdot\left(3^2\right)^5+\left(3.23\right)\cdot\left(2.2.2.3.5\right)}{\left(2^3\right)^4\cdot3^{12}-\left(2.3\right)^{11}}\)
\(=10\cdot\frac{2^{12}\cdot3^{10}+3^2.2^3.23.5}{2^{12}\cdot3^{12}-2^{11}.3^{11}}\)
\(=2.5\cdot\frac{2^3\cdot3^2\left(2^9.3^8+23.5\right)}{2^{11}.3^{11}\left(2.3-1\right)}\)
\(=\frac{2^4\cdot3^2.5\left(2^9.3^8+23.5\right)}{2^{11}.3^{11}.5}=\frac{3359347}{2^7.3^9}\)