1008³ - 3.1008².8 + 3.1008.8² - 2⁹

= 1008³ - 3.1008².8 + 3.1008.8² - 8³

= (1008 - 8)³

= 1000³

= 1000000000

=2016

3⁶ . 4⁶ = (3.4)⁶ = 12⁶

8² . 2³ . 16² = (2³)² . 2³ . (2⁴)

= 2⁶ . 2³ . 2⁴ = 2^{6 + 3 + 4} = 2¹³

2³ . 2² . 8³ = 2³ . 2² . (2³)³

= 2³ . 2² . 2⁹ = 2^{3 + 2 + 9} = 2¹⁴

y. y⁷ = y^{1 + 7} = y⁸

\(3^6\cdot4^6=\left(3\cdot4\right)^6=12^6\)

\(8^2\cdot2^3\cdot16^2=\left(2^3\right)^2\cdot2^3\cdot\left(2^4\right)^2\)

\(=2^6\cdot2^3\cdot2^8=2^{17}\)

\(2^3\cdot2^2\cdot8^3=2^5\cdot\left(2^3\right)^3\)

\(2^5\cdot2^9=2^{14}\)

\(y\cdot y^7=y^{1+7}=y^8\)

A=\(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{2013}-\frac{1}{2014}\)

tick đi mình giải cho

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

đáp số:50836

ai k mik mik sẽ k lại

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: \(C=\dfrac{5\cdot2^{30}\cdot3^{18}-2^{29}\cdot3^{20}}{5\cdot2^{35}\cdot3^{19}-7\cdot2^{29}\cdot3^{18}}\)

\(=\dfrac{2^{29}\cdot3^{18}\left(5\cdot2-3^2\right)}{2^{29}\cdot3^{18}\left(5\cdot2^6-7\right)}=\dfrac{10-9}{5\cdot64-7}=\dfrac{1}{313}\)