Rút gọn:
\(\frac{2^5.3^6+6^5.11}{12^5-6^5.2^2}\)
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MT
10 tháng 1 2016
\(\frac{7.4^5.3^{11}+2^{13}.9^5}{6^{10}+2^{12}.3^{10}}=\frac{7.\left(2^2\right)^5.3^{11}+2^{13}.\left(3^2\right)^5}{\left(2.3\right)^{10}+2^{12}.3^{10}}=\frac{7.2^{10}.3^{11}+2^{13}.3^{10}}{2^{10}.3^{10}+2^{12}.3^{10}}\)
\(=\frac{2^{10}.3^{10}.\left(7.3+2^3\right)}{2^{10}.3^{10}.\left(1+2^2\right)}=\frac{7.3+2^3}{1+2^2}=\frac{29}{5}\)
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\(\frac{2^5.3^6+6^5.11}{12^5-6^5.2^2}\)
\(=\frac{2^5.3^6+2^5.3^5.11}{2^2.3-2^5.3^5.2^2}\)
\(=\frac{2^5.3^5.\left(3+11\right)}{2^2.3\left(1-2^5.3^4\right)}\)
\(=\frac{2^3.3^4.14}{1-32.81}\)
\(=\frac{2^4.3^4.7}{-2591}\)
\(\frac{2^5\cdot3^6+6^5\cdot11}{12^5-6^5.2^2}\)
\(=\frac{6^5\cdot3+6^5\cdot11}{6^5\cdot2^5-6^5\cdot2^2}\)
\(=\frac{6^5\cdot\left(3+11\right)}{6^5\cdot\left(2^5-2^2\right)}\)
\(=\frac{14}{32-4}\)
\(=\frac{14}{28}=\frac{1}{2}\)