Ta có: 222333và333222
⇔((2223)111)và((3332)111)
=10941048111và110889111
vì 2 lũy thừa có cùng số mũ nên ta so sánh cơ số như so sánh số tự nhiên
Mặt khác vì 10941048>110889
Nên 10941048111>110889111
⇔2223>3332
Vậy 2223>3332
(222^3)^111=(2.111)^3=8.111^3=8.111.111^2=888.111^2
(333^2)^111=(3.111)^2=9.111^2
vậy 222^333>333^222
\(222^{333}=\left(2\cdot111\right)^{3\cdot111}=8^{111}\cdot\left(111^{111}\right)^2\cdot111^{111}\)
\(333^{222}=\left(3\cdot111\right)^{2\cdot111}=9^{111}\cdot\left(111^{111}\right)^2\)
vì \(8^{111}\cdot\left(111^{111}\right)^2\cdot111^{111}>9^{111}\cdot\left(111^{111}\right)^2\)
\(\Rightarrow222^{333}>333^{222}\)
Ta có:
\(222^{333}=\left(222^3\right)^{111}=10941048^{111}\)
\(333^{222}=\left(333^2\right)^{111}=110889^{111}\)
Ta thấy: \(10941048>110889\)
\(\Leftrightarrow10941048^{111}>110889^{111}\)
\(\Leftrightarrow222^{333}>333^{222}\)
Vậy \(222^{333}>333^{222}\)
Ta có 222333=(2223)111=10941048111
và 333222=(3332)111=110889111
Vì 10941048>110889.suy ra 222333>333222
Vây ................
