Câu hỏi của Lô Thị Cú Mèo

Question

1, So sanh : $222^{777}$; $777^{222}$

Nguyên Anh · Accepted Answer

$222^{777}=2^{777}.111^{777}=\left(2^7\right)^{111}.111^{777}=128^{111}.111^{777}$

$777^{222}=7^{222}.111^{222}=\left(7^2\right)^{111}.111^{222}=49^{111}.111^{222}$

Vì $128^{111}.111^{777}>49^{111}.111^{222}$ nên $222^{777}>777^{222}$

Câu trả lời:

$222^{777}=2^{777}.111^{777}=\left(2^7\right)^{111}.111^{777}=128^{111}.111^{777}$

$777^{222}=7^{222}.111^{222}=\left(7^2\right)^{111}.111^{222}=49^{111}.111^{222}$

Vì $128^{111}.111^{777}>49^{111}.111^{222}$ nên $222^{777}>777^{222}$