Question

So sánh:

222³³³ và 333²²²

Trình bày cụ thể nha~

Answer 1

222³³³ = 222^3.111 = ( 222³ )¹¹¹ = 10941048¹¹¹

333²²² = 333^2.111 = ( 333² )¹¹¹ = 110889¹¹¹

mà 10941048¹¹¹ > 110889¹¹¹ => 222³³³ > 333²²²

Answer 2

Ta có : \(222^{333}=222^{3.111}=\left(222^3\right)^{111}\)

           \(333^{222}=333^{2.111}=\left(333^2\right)^{111}\)

Ta so sánh : \(222^3\) và \(333^2\)

\(222^3=\left(2.111\right)^3=2^3.111^3=8.111^3=888.111^2\)

\(333^2=\left(3.111\right)^2=3^2.111^2=9.111^2\)

Vì   \(888>9\) \(\Rightarrow\) \(888.111^2>9.111^2\)  

\(\Rightarrow\) \(222^3< 333^2\)    \(\Rightarrow\)  \(222^{333}< 333^{222}\)