Rút gọn phân số:
A = \(\frac{2^{13}.9-2^{12}.5}{2^{12}.6+2^{12}.7}\)
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NL
Nguyễn Lê Phước Thịnh
CTVHS
25 tháng 2
a: \(\frac{3^{10}\cdot\left(-5\right)^{21}}{\left(-5\right)^{20}\cdot3^{12}}=\frac{-3^{10}\cdot5^{21}}{3^{12}\cdot5^{20}}=\frac{-5}{3^2}=-\frac59\)
b: \(\frac{-11^5\cdot13^7}{11^5\cdot13^8}=\frac{-11^5}{11^5}\cdot\frac{13^7}{13^8}=-\frac{1}{13}\)
c: \(2^{10}\cdot3^{10}-2^{10}\cdot3^9\)
\(=2^{10}\cdot3^9\cdot\left(3-1\right)\)
\(=2^{11}\cdot3^9\)
Ta có: \(\frac{2^{10}\cdot3^{10}-2^{10}\cdot3^9}{2^9\cdot3^{10}}\)
\(=\frac{2^{11}\cdot3^9}{2^{10}\cdot3^9}=2\)
d: \(5^{11}\cdot7^{12}+5^{11}\cdot7^{11}\)
\(=5^{11}\cdot7^{11}\left(7+1\right)=5^{11}\cdot7^{11}\cdot8\)
\(5^{12}\cdot7^{12}+9\cdot5^{11}\cdot7^{11}\)
\(=5^{11}\cdot7^{11}\left(5\cdot7+9\right)\)
\(=5^{11}\cdot7^{11}\left(35+9\right)=5^{11}\cdot7^{11}\cdot44\)
Ta có: \(\frac{5^{11}\cdot7^{12}+5^{11}\cdot7^{11}}{5^{12}\cdot7^{12}+9\cdot5^{11}\cdot7^{11}}\)
\(=\frac{5^{11}\cdot7^{11}\cdot8}{5^{11}\cdot7^{11}\cdot44}=\frac{8}{44}=\frac{2}{11}\)
MT
10 tháng 1 2016
\(\frac{7.4^5.3^{11}+2^{13}.9^5}{6^{10}+2^{12}.3^{10}}=\frac{7.\left(2^2\right)^5.3^{11}+2^{13}.\left(3^2\right)^5}{\left(2.3\right)^{10}+2^{12}.3^{10}}=\frac{7.2^{10}.3^{11}+2^{13}.3^{10}}{2^{10}.3^{10}+2^{12}.3^{10}}\)
\(=\frac{2^{10}.3^{10}.\left(7.3+2^3\right)}{2^{10}.3^{10}.\left(1+2^2\right)}=\frac{7.3+2^3}{1+2^2}=\frac{29}{5}\)
\(A=\frac{2^{13}.9-2^{12}.5}{2^{12}.6+2^{12}.7}\)
\(=\frac{2^{12}.\left(2.9-5\right)}{2^{12}.\left(6+7\right)}\)
\(=\frac{2^{12}.\left(18-5\right)}{2^{12}.13}\)
\(=\frac{2^{12}.13}{2^{12}.13}=1\)