\(G=1+2012+2012^2+2012^3+2012^4+...+2012^{71}+2012^{72}\)

\(\Rightarrow G=\dfrac{2012^{72+1}-1}{2012-1}\)

\(\Rightarrow G=\dfrac{2012^{73}-1}{2011}< H=2012^{73}-1\)

\(12^8=\left(12^2\right)^4=144^4\)

\(8^{12}=\left(8^3\right)^4=512^4\)

Vì \(144^4< 512^4\)nên \(12^8< 8^{12}\)

8^12=64^8

vì 64^8>12^8

=>12^8<8^12

hok tốt

12⁸ và 8¹²

12⁸ = (12²)⁴ = 144⁴

8¹² = (8³)⁴ = 512⁴

Vì 144⁴ < 512⁴ nên 12⁸ < 8¹²

ta có:

\(81^{12}=\left(3^4\right)^{12}=3^{38}\)

\(27^{13}=\left(3^3\right)^{13}=3^{39}\)

vì \(38< 39=>3^{38}< 3^{39}=>81^{12}< 27^{13}\)

vậy \(81^{12}< 27^{13}\)

81^12=3^(4.12)=3^48

27^13=3^(3.13)=3^39

Có 3^48>3^39 nên 81^12>27^13

ta có:

\(81^{12}=\left(3^4\right)^{12}=3^{38}\)

a) Vì \(-45< -16\) nên \(\left(-\dfrac{45}{17}\right)^{15}< \left(\dfrac{-16}{17}\right)^{15}\)

b) Vì \(21< 23\) nên \(\left(-\dfrac{8}{9}\right)^{21}< \left(-\dfrac{8}{9}\right)^{23}\)

c) \(27^{40}=3^{3^{40}}=3^{120}\)

\(64^{60}=8^{2^{60}}=8^{120}\)

Vì \(3< 8\) nên \(3^{120}< 8^{120}\) hay \(27^{40}< 64^{60}\)

con ai kooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo

co don quaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa

Rút gọn phân số (nhưng không tối giản phân số) \(\dfrac{8}{12}\), ta được:

\(\dfrac{8}{12}=\dfrac{8:2}{12:2}=\dfrac{4}{6}\)

Vậy ta so sánh \(\dfrac{4}{6};\dfrac{4}{5}\)

Vì \(6>5\) nên \(\dfrac{4}{6}< \dfrac{4}{5}\) hay \(\dfrac{8}{12}< \dfrac{4}{5}\)

Kết luận: \(\dfrac{8}{12}< \dfrac{4}{5}\)

8/12=2/3=4/6<4/5

a , ta có : 8¹² = ( 4 . 2 )¹² = 4²⁴

12⁸ = ( 4 . 3 ) ⁸ = 4²⁴

vì 24 = 24 nên 4^24 = 4^24

do đó 8^12 = 12^8 ..

K BIẾT CÓ ĐÚNG K NỮA

AI K MIK MIK K LẠI

a)\(12^8=\left(12^2\right)^4=144^4\)

\(8^{12}=\left(8^3\right)^4=512^4\)

\(144^4< 512^4\Rightarrow12^8< 8^{12}\)

b)\(\left(-5\right)^{39}=\left[\left(-5\right)^3\right]^{13}=\left(-125\right)^{13}\)

\(\left(-2\right)^{91}=\left[\left(-2\right)^7\right]^{13}=\left(-128\right)^{13}\)

\(\left(-125\right)^{13}>\left(-128\right)^{13}\Rightarrow\left(-5\right)^{39}>\left(-2\right)^{91}\)

:((

8/12=2/3=4/6<4/5

Vì 4.12  = 6.8 nên \(\frac{4}{6} = \frac{8}{{12}}\)

Vì 8.(-15) = 12. (-10) nên \(\frac{8}{{12}} = \frac{{ - 10}}{{ - 15}}\)

Vì 4.(-15) = 6.(-10) nên \(\frac{4}{6} = \frac{{ - 10}}{{ - 15}}\)