Ta có :
\(333^{444}=\left(3.111\right)^{444}=3^{444}.111^{444}=\left(3^4\right)^{111}.111^{444}=81^{111}.111^{444}\)
\(444^{333}=\left(4.111\right)^{333}=4^{333}.111^{333}=\left(4^3\right)^{111}.111^{333}=64^{111}.111^{333}\)
Vì \(81^{111}>64^{111}\) và \(111^{444}>111^{333}\)
nên \(81^{111}.111^{444}>64^{111}.111^{333}\)
Vậy \(333^{444}>444^{333}\)
tích mình nha !!!
A=333^444=111^3.444=111^1332
B=444^333=111^4.333=111^1332
=>A=B
Ta có :
\(33 3^{444} = \left(\left(\right. 3.111 \left.\right)\right)^{444} = 3^{444} . 11 1^{444} = \left(\left(\right. 3^{4} \left.\right)\right)^{111} . 11 1^{444} = 8 1^{111} . 11 1^{444}\)
\(44 4^{333} = \left(\left(\right. 4.111 \left.\right)\right)^{333} = 4^{333} . 11 1^{333} = \left(\left(\right. 4^{3} \left.\right)\right)^{111} . 11 1^{333} = 6 4^{111} . 11 1^{333}\)
Vì \(8 1^{111} > 6 4^{111}\) và \(11 1^{444} > 11 1^{333}\)
nên \(8 1^{111} . 11 1^{444} > 6 4^{111} . 11 1^{333}\)
Vậy \(33 3^{444} > 44 4^{333}\)
tích mình nha !!!
