Rút gọn hợp lí
a) \(M=\frac{131\times145+100}{45-132\times145}\)
b)\(N=\frac{49^6\times5-7^{11}}{\left(-7\right)^{10}\times5+2\times49^5}\)
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\(M=\frac{131.145+100}{45-132.145}\)
\(=\frac{131-\frac{100}{145}}{\frac{45}{145}-132}\)
\(=\frac{131-\frac{20}{29}}{\frac{9}{29}-132}\)
\(=\frac{131\frac{-20}{29}}{-132\frac{9}{29}}\)
\(a)\frac{3^{10}.\left(-5\right)^{21}}{\left(-5\right)^{20}.3^{12}}=\frac{-5}{3^2}=\frac{-5}{9}\)
\(b)\frac{-11.13^7}{11^5.13^8}=\frac{-1}{11^4.13}\) (Bạn xem thử xem có sai đề không nhé)
\(c)\frac{2^{10}.3^{10}-2^{10}.3^9}{2^9.3^{10}}=\frac{2^{10}.3^9\left(3+1\right)}{2^9.3^{10}}=\frac{2.4}{3}=\frac{8}{3}\)
\(d)\frac{5^{11}.7^{12}+5^{11}.7^{11}}{5^{12}.7^{12}+9.5^{11}.7^{11}}=\frac{5^{11}.7^{11}\left(7+1\right)}{5^{11}.7^{11}\left(5.4+9\right)}=\frac{8}{20+9}=\frac{8}{29}\)
\(a)\frac{3^{10}\cdot\left(-5\right)^{21}}{\left(-5\right)^{20}\cdot3^{12}}=\frac{-5}{3^2}=\frac{-5}{9}\)
\(b)\frac{\left(-11\right)\cdot13^7}{11^5\cdot13^8}=\frac{-1}{11^4\cdot13}=\frac{-1}{14641\cdot13}=\frac{-1}{190333}\)
\(c)\frac{2^{10}\cdot3^{10}-2^{10}\cdot3^9}{2^9\cdot3^{10}}=\frac{2^{10}\left(3^{10}-3^9\right)}{2^9\cdot3^{10}}=\frac{2^{10}\cdot3^9\left(3-1\right)}{2^9\cdot3^{10}}=\frac{2^{10}\cdot3^9\cdot2}{2^9\cdot3^{10}}=\frac{2\cdot2}{3}=\frac{4}{3}\)
Đặt \(A=\frac{1}{1.2.3}+\frac{1}{3.5.7}+...+\frac{1}{45.47.49}\)
\(\Rightarrow4A=\frac{4}{1.3.5}+\frac{4}{3.5.7}+...+\frac{4}{45.47.49}\)
\(=\frac{1}{1.3}-\frac{1}{3.5}+\frac{1}{3.5}-\frac{1}{5.7}+...+\frac{1}{45.47}-\frac{1}{47.49}\)
\(=\frac{1}{3}-\frac{1}{47.49}\)
\(\Rightarrow A=\frac{\frac{1}{3}-\frac{1}{47.49}}{4}=\frac{575}{6909}\)
\(\Rightarrow\)C . \(\frac{2}{3}\) =\(\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}\)....+\(\frac{2}{47.49}\)
\(\Rightarrow C.\frac{2}{3}=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+.....+\frac{1}{47}-\frac{1}{49}\)
\(\Rightarrow C=\left(\frac{1}{3}-\frac{1}{49}\right)\div\frac{2}{3}\)
\(\Rightarrow C=\frac{46}{147}\div\frac{2}{3}\)
\(\Rightarrow C=\frac{23}{49}\)
Vậy C = \(\frac{23}{49}\)
nếu đúng từ mk xin 1 chữ đúng và
\(\frac{131.145+100}{45-132.140}=\frac{132.145-45}{45-132.140}=-1\)
\(\frac{49^6.5-7^{11}}{\left(-7\right)^{10}.5+2.49^5}=\frac{7^{11}.7-7^{11}.1}{7^{10}.5+2.7^{10}}=\frac{7^{11}.\left(7-1\right)}{7^{10}.\left(5+2\right)}=\frac{7^{11}.6}{7^{11}}=6\)
1 x 3 x 5 + 2 x 6 x 10 + 4 x 10 x 12 + 7 x 21 x 35 / 1 x 5 x 7 + 2 x 10 x 14 + 4 x 20 x 28 + 7 x 35 x 49
= 3 / 7 + 6 / 14 + 10 x 2 x 6 / 10 x 2 x 28 + 21 / 49
= 3 / 7 + 6 / 14 + 6 / 28 + 21 / 49
= 3 / 7 + 6 / 14 + 3 / 14 + 3 / 7
= ( 3 / 7 + 3 / 7 ) + ( 6 / 14 + 3 / 14 )
= 6 / 7 + 9 14
= 12 / 14 + 9 / 14
= 21 / 14
nho hem
lm dau tien lun do
dung 100% nha