`@` `\text {Answer}`

`\downarrow`

Ta có:

\(333^{444}=\left(333^4\right)^{111}=\left(3^4\cdot111^4\right)^{111}=\left(81\cdot111^4\right)^{111}=81^{111}\cdot111^{444}\)   `(1)`

\(444^{333}=\left(444^3\right)^{111}=\left(4^3\cdot111^3\right)^{111}=\left(64\cdot111^3\right)=64^{111}\cdot111^{333}\) `(2)`

Vì \(81>64\), \(444>333\) 

`=>`\(81^{111}>64^{111},\) \(111^{444}>111^{333}\) `(3)`

Từ `(1), (2)` và `(3)`

`=>`\(333^{444}>444^{333}\)

333^444>444^333

Ta có: 333^444= 111^444 x 3^444 
444^333 = 111^333 x 4^333 
Tách: 3^444 = (3^4)^111 =81^111 <=>4^333 = (4^3)^111 = 64^111 
Mà: {111^444 > 111^333 (1) 
{81^111 > 64^111 hay: (3^4)^111 > (4^3)^111 (2) 
Từ (1) và (2) ta có:333^444 > 444^333 

> 

chúc bạn học tốt

\(333^{444}\)và \(444^{333}\)

Ta có:

\(\Rightarrow\)\(333^{444}=\left(333^4\right)^{111}\)

\(\Rightarrow\)\(444^{333}=\left(444^3\right)^{111}\)

111 đã có cùng số mũ nên ta so sánh \(\left(333^4\right)\)và \(\left(444^3\right)\)ta đc:

\(\Rightarrow\)\(333^4=\left(3.111\right)^4=3^4.111^4=81.111^4\)

\(\Rightarrow\)\(444^3=\left(4.111\right)^3=4^3.111^3=64.111^3\)

Vì: \(81.111^4>61.111^3\)

\(\Rightarrow\)\(333^{444}>444^{333}\)

Ta có: \(81=3^4>4^3=64\)

\(\Rightarrow4^3\cdot111^3< 3^4\cdot111^3< 3^4\cdot111^4\)

\(\Rightarrow444^3< 333^4\)

\(\Rightarrow\left(444^3\right)^{111}< \left(333^4\right)^{111}\)

\(\Rightarrow444^{333}< 333^{444}\)

\(\Rightarrow-333^{444}< -444^{333}\)

\(333^{444}=\left(111.3\right)^{444}=111^{444}.3^{444}\)

\(444^{333}=\left(111.4\right)^{333}=111^{333}.4^{333}\)

mà \(3^{444}=3^{4.111}=81^{111}\)

\(4^{333}=4^{3.111}=64^{111}\)

ta có : \(111^{444}>111^{333}\)

\(81^{111}>64^{111}\)

\(\Rightarrow333^{444}>444^{333}\)

Ta có: \(333^{444}=\left(3.111\right)^{444}=3^{444}.111^{444}\)

          \(444^{333}=\left(4.111\right)^{333}=4^{333}.111^{333}\)

Ta lại có: \(3^{444}=\left(3^4\right)^{111}=81^{111}\)

               \(4^{333}=\left(4^3\right)^{111}=64^{111}\)

\(\Rightarrow3^{444}>4^{333}\left(81^{111}>64^{111}\right)\)

Mặt khác: \(111^{444}>111^{333}\)

\(\Rightarrow3^{444}.111^{444}>4^{333}.111^{333}\)

Vậy \(333^{444}>444^{333}\)

ta có : 333⁴⁴⁴ = (333⁴)¹¹¹

          444³³³ = (444³)¹¹¹

Ta so sánh: 333⁴ và 444³ 

Khi đó: 333⁴ = (3.111)⁴ = 3⁴.111⁴ =81.111³

              444³ = (4.111)³ = 4³.111³ =64.111³

81.111³ > 64.111³

=> 333⁴⁴⁴ > 444³³³

nha bạn chúc bẠN CHÚC BẠN HỌC TỐT NHA 

333^444>444^333

dấu  > nhé bạn vì mình ko ghi được giữa hai chữ số bên mọi thông cảm.