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\(\frac{10^3+2.5^3+5^3}{55}-\frac{4^6.9^5+6^9.120}{8^4.3^{12}-6^{11}}\)\(=\frac{2^3.5^3+2.5^3+5^3}{5.11}-\frac{2^{12}.3^{10}+2^9.3^9.2^3.3.5}{2^{12}.3^{12}-2^{11}.3^{11}}\)
\(=\frac{5^3\left(2^3+2+1\right)}{5.11}-\frac{2^{12}.3^{10}.\left(1+5\right)}{2^{11}.3^{11}.\left(2.3-1\right)}=\frac{5^2.11}{11}-\frac{2.6}{3.5}=25-\frac{4}{5}=\frac{121}{5}\)
\(10\cdot\frac{4^6\cdot9^5+6^9\cdot120}{8^4\cdot3^{12}-6^{11}}\)
\(=10\cdot\frac{2^{12}\cdot3^{10}+2\cdot9\cdot3^9\cdot2^3\cdot3\cdot5}{2^{12}.3^{12}-2^{11}.3^{11}}\)
\(=10\cdot\frac{2^{12}\cdot3^{10}\cdot\left(1+5\right)}{2^{11}\cdot3^{11}\cdot\left(2\cdot3-1\right)}\)
\(=10\cdot\frac{2\cdot6}{3\cdot5}=8\)
\(\frac{4^6.9^5+6^9.120}{8^4.3^{12}-6^{11}}.10=\frac{2^{12}.3^{10}+2^9.3^9.120}{2^{12}.3^{12}-2^{11}.3^{11}}.10=\frac{2^{10}.3^{10}\left(2^2+20\right)}{2^{10}.3^{10}\left(6^2-6\right)}.10=\frac{24.10}{30}=8\)
Đầu tiên ta rút gọn \(\frac{4^{^6}.9^{^5}+6^{^9}.120}{8^{^4}.3^{^{12}}-6^{^{11}}}\)= \(\frac{2^{^{12}}.3^{^{10}}+2^{^9}.3^{^9}.2^{^3}.3.5}{2^{^{12}}.3^{^{12}}-2^{^{11}}-3^{^{11}}}\)= \(\frac{2^{^{12}}.3^{^{10}}+2^{^{12}}.3^{^{10}}.5}{2^{^{12}}.3^{^{12}}-2^{^{11}}.3^{^{11}}}\)= \(\frac{2^{^{12}}.3^{^{10}}.\left(1+5\right)}{2^{^{11}}.3^{^{11}}.\left(6-1\right)}\)= \(\frac{2.6}{3.5}\)= \(\frac{12}{15}\)= \(\frac{4}{5}\)
\(\Rightarrow\)10 . \(\frac{4}{5}\)= \(\frac{40}{5}\)= 8
