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\(10.\frac{\left(2^2\right)^6.\left(3^3\right)^5+\left(2.3\right)^9.\left(2^3.3.5\right)}{\left(2^4\right)^3.3^{12}-\left(2.3\right)^{11}}\)
\(=10.\frac{2^{12}.3^{15}+2^{12}.3^{10}.5}{2^{12}.3^{12}-2^{11}.3^{11}}\)
\(=10.\frac{2^{12}.3^{10}\left(3^5+1.5\right)}{2^{11}.3^{11}\left(2.3-1\right)}\)
\(=10\frac{2\left(3^5+5\right)}{3.5}\)
\(=10.\frac{496}{15}\)
\(=\frac{992}{3}\)
Study well
10.\(\frac{241864704+1209323520}{2176782336-6^{11}}\)
=10.\(\frac{362797224}{1813985280}\)
=2,000000926
\(10\cdot\frac{4^6\cdot9^5+6^9\cdot120}{8^4\cdot3^{12}-6^{11}}\)
\(=10\cdot\frac{2^{12}\cdot3^{10}+2\cdot9\cdot3^9\cdot2^3\cdot3\cdot5}{2^{12}.3^{12}-2^{11}.3^{11}}\)
\(=10\cdot\frac{2^{12}\cdot3^{10}\cdot\left(1+5\right)}{2^{11}\cdot3^{11}\cdot\left(2\cdot3-1\right)}\)
\(=10\cdot\frac{2\cdot6}{3\cdot5}=8\)
\(\frac{4^6.9^5+6^9.120}{8^4.3^{12}-6^{11}}.10=\frac{2^{12}.3^{10}+2^9.3^9.120}{2^{12}.3^{12}-2^{11}.3^{11}}.10=\frac{2^{10}.3^{10}\left(2^2+20\right)}{2^{10}.3^{10}\left(6^2-6\right)}.10=\frac{24.10}{30}=8\)