\(333^{444}=\left(3.111\right)^{^{444}}=3^{444}.111^{444}=\left(3^4\right)^{111}.111^{444}=81^{111}.111^{444}\)
\(444^{333}=\left(4.111\right)^{333}=4^{333}.111^{333}=\left(4^3\right)^{111}.111^{333}=64^{111}.111^{333}\)
Vì 81 > 64 nên 81111 > 64111 và 111444 > 111333
=> 81111.111444 > 64111.111333
=> \(333^{444}>444^{333}\)
2 cách:
Cách 1:
333444=(3334)111=12296370321111
444333=(4443)111=87528384111
vì 12296370321>87528384 nên 12296370321111>87528384111
hay 333444>444333
Cách 2:
Ta có : 333444=(3.111)444=3444.111444
444333=(4.111)333=4333.111333
ta lại có: 3444=(34)111=81111
4333=(43)111=64111
=>3444>4333 ( vì 81111>64111)
mặt khác 111444>111333(vì 444>333)
suy ra : 3444.111444>4333.111333
hay 333444>444333
ta có:
333444=(3334)111
444333=(4443)111
=> 3334=(3.111)4=34.1114=81.1114
4443=(4.111)3=43.1113=64.1113
vì 81.1114>64.1113 nên 3334>4443
vậy 333444>444333
