Question

[Na]

So sánh 

333⁴⁴⁴ va 444³³³

Answer 1

[Minh Chương]

333⁴⁴⁴ > 444³³³ 

k mik nha

Answer 2

[Phạm Hàn Minh Chương]

A = : \(333^{444}\)= \(\left(111\cdot3\right)^{444}\)=\(111^{444}\)x\(3^{444}\)

= \(\left(111^4\right)^{111}\)x \(\left(3^4\right)^{111}\)=  \(\left(111^4\right)^{111}\cdot81^{111}\).

B = : \(444^{333}\)= \(\left(111\cdot4\right)^{333}\)=  \(111^{333}\)x  \(4^{333}\)=  \(\left(111^3\right)^{111}\)x \(\left(4^3\right)^{111}\)

=  \(\left(111^3\right)^{111}\cdot64^{111}\)

Ta có : \(\left(111^4\right)^{111}\cdot81^{111}và\left(111^3\right)^{111}\cdot64^{111}\)

Vì \(\left(111^4\right)^{111}>\left(111^3\right)\:^{111}\)và   \(81^{111}>64^{111}\)

=> \(\left(111^4\right)^{111}\cdot81^{111}>\left(111^3\right)^{111}\cdot64^{111}\)

Vậy \(333^{444}>444^{333}\)Chúc cậu học tốt !!!