1008^3-3.1008^2.8+3.1008.8^2-2^6
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1008³ - 3.1008².8 + 3.1008.8² - 2⁹
= 1008³ - 3.1008².8 + 3.1008.8² - 8³
= (1008 - 8)³
= 1000³
= 1000000000
![](https://rs.olm.vn/images/avt/0.png?1311)
36 . 46 = (3.4)6 = 126
82 . 23 . 162 = (23)2 . 23 . (24)
= 26 . 23 . 24 = 26 + 3 + 4 = 213
23 . 22 . 83 = 23 . 22 . (23)3
= 23 . 22 . 29 = 23 + 2 + 9 = 214
y. y7 = y1 + 7 = y8
\(3^6\cdot4^6=\left(3\cdot4\right)^6=12^6\)
\(8^2\cdot2^3\cdot16^2=\left(2^3\right)^2\cdot2^3\cdot\left(2^4\right)^2\)
\(=2^6\cdot2^3\cdot2^8=2^{17}\)
\(2^3\cdot2^2\cdot8^3=2^5\cdot\left(2^3\right)^3\)
\(2^5\cdot2^9=2^{14}\)
\(y\cdot y^7=y^{1+7}=y^8\)
![](https://rs.olm.vn/images/avt/0.png?1311)
A=\(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{2013}-\frac{1}{2014}\)
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1+2+3+4+5+6+7+8+9+........+1008
=(1+1008)*[(1008-1):1+1]:2
=1009*1008:2
=1009*504
=50836
nếu thấy đúng thì k cho mh nah
1-1/2+1/3-1/4+1/5-1/6+...+1/2011-1/2012 / 1006-1006/1007-1007/1008-1008/1009-...-2010/2011-2011/2012
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a: \(A=\dfrac{3^3\cdot2^3+3^3\cdot2^2+3^3\cdot1}{-13}=\dfrac{27\left(2^3+2^2+1\right)}{-13}=-27\)
b: \(B=\dfrac{2\cdot2^{12}\cdot3^6+2^{11}\cdot3^9}{2^3\cdot2^7\cdot3^7+2^7\cdot2^3\cdot5\cdot3^8}\)
\(=\dfrac{2^{13}\cdot3^6+2^{11}\cdot3^9}{2^{10}\cdot3^7+2^{10}\cdot5\cdot3^8}\)
\(=\dfrac{2^{11}\cdot3^6\left(2^2+3^3\right)}{2^{10}\cdot3^7\left(1+5\cdot3\right)}=\dfrac{2}{3}\cdot\dfrac{4+27}{1+15}=\dfrac{2}{3}\cdot\dfrac{31}{16}=\dfrac{31}{24}\)
c: \(C=\dfrac{5\cdot2^{30}\cdot3^{18}-2^{29}\cdot3^{20}}{5\cdot2^{35}\cdot3^{19}-7\cdot2^{29}\cdot3^{18}}\)
\(=\dfrac{2^{29}\cdot3^{18}\left(5\cdot2-3^2\right)}{2^{29}\cdot3^{18}\left(5\cdot2^6-7\right)}=\dfrac{10-9}{5\cdot64-7}=\dfrac{1}{313}\)
\(1008^3-3\cdot1008^2+8+3\cdot1008\cdot8^2-2^6\)
\(=\left(1008-8\right)^3\)
=1000000000
mình nghĩ kết quả ra (1008-8^2)^3