\(333^{444}=333^{111.4}=\left(333^4\right)^{111}=\text{12296370321}^{111}\)
\(444^{333}=444^{111.3}=\left(444^3\right)^{111}=\text{87528384}^{111}\)
Vì \(12296370321>\text{87528384}\) nên \(12296370321^{111}>\text{87528384}^{111}\)hay \(333^{444}>444^{333}\)
333444 = 111444 . 3444 = 111444 . (34)111 = 111444 . 81111
444333 = 111333 . 4333 = 111333 . (43)111 = 111333 . 64111
Vì 111444 . 81111 > 111333 . 64111
=> 333444 > 444333
ta có : \(333^{444}=\left(333^4\right)^{111}\)
\(444^{333}=\left(444^3\right)^{111}\)
mà \(333^4< 444^3\)===>\(\left(333^4\right)^{111}< \left(444^3\right)^{111}\)
nên \(333^{444}< 444^{333}\)
333444 = 111444 . 3444 = 111444 . (34)111 = 111444 . 81111
444333 = 111333 . 4333 = 111333 . (43)111 = 111333 . 64111
Vì 111444 . 81111 > 111333 . 64111
=> 333444 > 444333
