\(2222^{5555}=2^{5555}.1111^{5555}=\left(2^5\right)^{1111}.1111^{5555}=32^{1111}.1111^{5555}\)
\(5555^{2222}=5^{2222}.1111^{2222}=\left(5^2\right)^{1111}.1111^{2222}=25^{1111}.1111^{2222}\)
\(32^{1111}.1111^{5555}>25^{1111}.1111^{2222}\Rightarrow2222^{5555}>5555^{2222}\)
vậy \(2222^{5555}>5555^{2222}\)
\(2222^{5555}=2222^{5.11}=\left(2222^5\right)^{1111}\)
\(5555^{2222}=5555^{2.1111}=\left(5555^2\right)^{1111}\)
Để
So sánh : 2222^5555 và 5555^2222 ta cần so sánh 2222^5 và 5555^2
\(2222^5=2^5.1111^5=32.1111^5\)
\(5555^2=5^2.1111^2=25.1111^2\)
Vì \(32>25;1111^5>1111^2\Rightarrow32.1111^5>25.1111^2\Rightarrow2222^5>5555^2\Rightarrow2222^{5555}>5555^{2222}\)
