Câu hỏi của kieu the bao

Question

So sánh

$222^{555}$va $555^{222}$

ミ★ɦυүềη☆bùї★彡 · Accepted Answer

Ta có $222^{555}=\left(222^5\right)^{111}=\left(2^5.111^5\right)^{111}=\left(32.111^5\right)^{111}$

$555^{222}=\left(555^2\right)^{111}=\left(5^2.111^2\right)^{111}=\left(25.111^2\right)^{111}$

Do $32.111^5>25.111^2$ nên $222^{555}>555^{222}$

Câu trả lời:

Ta có $222^{555}=\left(222^5\right)^{111}=\left(2^5.111^5\right)^{111}=\left(32.111^5\right)^{111}$

$555^{222}=\left(555^2\right)^{111}=\left(5^2.111^2\right)^{111}=\left(25.111^2\right)^{111}$

Do $32.111^5>25.111^2$ nên $222^{555}>555^{222}$