\(333^{444}=333^{3^{111}}\)
\(444^{333}=444^{3^{111}}\)
Vì \(444^{3^{111}}>333^{3^{111}}\)
=> \(333^{444}< 444^{333}\)
Ta có: \(333^{444}=\left(333^4\right)^{111}\)
\(444^{333}=\left(444^3\right)^{111}\)
Vì 333444 và 444333 có cùng số mũ là 111. nên ta so sánh 3334 và 4443
3334=(3.111)4=34.1114=81.1114
4443=(4.111)3=43.1113=64.1113
Vì 81.1114>64.1113 => 3334>4443
=> 333444 > 444333
\(333^{444}=\left(333^4\right)^{111}=\left[\left(3.111^4\right)\right]^{111}=\left[3^4.111^4\right]^{111}=\left[81.111^4\right]^{111}\)
\(444^{333}=\left(444^3\right)^{111}=\left[\left(4.111\right)^3\right]^{111}=\left[4^3.111^3\right]^{111}=\left[64.111^3\right]^{111}\)
Vì (81.1114)111 > (64.1113)111 nên 333444 > 444333
