Question

[Phan Ngọc Khuê]

so sánh \(222^{555}\&555^{222}\)

Answer 1

[Minh Hiền]

\(222^{555}=\left(2.111\right)^{555}=2^{555}.111^{555}=\left(2^5\right)^{111}.111^{555}=32^{111}.111^{555}\)

\(555^{222}=\left(5.111\right)^{222}=5^{222}.111^{222}=\left(5^2\right)^{111}.111^{222}=25^{111}.111^{222}\)

Vì 32¹¹¹ > 25¹¹¹ và 111⁵⁵⁵ > 111²²²

=> \(32^{111}.111^{555}>25^{111}.111^{222}\)

Vậy \(222^{555}>555^{222}\).