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\(\frac{4^{15}.3^{12}+120.8^3}{2^3.3^9-27.2^4}\)
\(=\frac{2^{30}.3^{12}+2^3.3.5.2^9}{2^3.3^9-3^3.2^4}\)
\(=\frac{2^{30}.3^{12}+2^{12}.3.5}{2^3.3^3\left(3^6-2\right)}\)
\(=\frac{2^{12}.3\left(2^8.3^{11}+5\right)}{2^3.3^3.727}\)
\(=\frac{2^9\left(2^8.3^{11}+5\right)}{3^2.727}\)
đến đây dễ rồi bạn tự làm đi
a,M=2^0-2^1+2^2-2^3+2^4-2^5+.....+2^2012
2M=2^1-2^2+2^3-2^4+2^5-2^5+......-2^2012+2^2013
3M=2^0+2^2013
M=(2^0+2^2013)÷3
Vậy.......
b,N=3-3^2+3^3-3^4+3^5-3^6+.....+3^2011-3^2012
3N=3^2-3^3+3^4-3^5+3^6-3^7+......+3^2012-3^2013
4N=3-3^2013
N=(3-3^2013)÷4
Vậy........
K tao nhé ko lên lớp tao đánh m😈😈😈
\(\frac{3.8\left(-14\right)}{42.35}\)
\(=\frac{3.2.4.\left(-1\right).7.2}{2.3.7.5.7}\)
\(=-\frac{8}{35}\)
\(\frac{2^7.91-2^6.20}{3^3.12+3^4.28}=\frac{2^6.2.91-2^6.20}{3^3.12+3^3.3.28}=\frac{2^6.189-2^6.20}{3^3.12+3^3.84}=\frac{2^6.\left(189-20\right)}{3^3.\left(12+84\right)}=\frac{2^6.169}{3^3.96}\)
\(A=\frac{2^{15}.3^{12}-3^{11}.2^{17}}{2^{15}.3^{11}+3^{11}.2^{17}}\)
\(A=\frac{2^{15}.3^{11}.\left(3-2^2\right)}{2^{15}.3^{11}.\left(1+2^2\right)}\)
\(A=\frac{3-2^2}{1+2^2}\)
\(A=\frac{-1}{5}\)
a) \(A=1+3+3^2+...+3^{100}\)
\(3A=3+3^2+3^3+...+3^{101}\)
\(3A-A=\left(3+3^2+3^3+...+3^{101}\right)-\left(1+3+3^2+...+3^{100}\right)\)
\(2A=3^{101}-1\)
\(A=\frac{3^{101}-1}{2}\)
b) \(B=2^{100}-2^{99}+2^{98}-2^{97}+...-2^3+2^2-2+1\)
\(2B=2^{101}-2^{100}+2^{99}-2^{98}+...-2^4+2^3-2^2+2\)
\(B+2B=\left(2^{100}-2^{99}+...-2+1\right)+\left(2^{101}-2^{100}+...-2^2+2\right)\)
\(3B=2^{101}+1\)
\(B=\frac{2^{101}+1}{3}\)