a)

333⁴⁴⁴=(3.111)^4.111=(27.111⁴)¹¹¹=(27.111.111³)¹¹¹

444³³³=(4.111)^3.111=(64.111³)¹¹¹

=>333⁴⁴⁴>444³³³

a) Do 300 < 450

⇒ 3³⁰⁰ < 3⁴⁵⁰

b) 333⁴⁴⁴ = (333⁴)¹¹¹ = (111⁴.3⁴)¹¹¹

444³³³ = (444³)¹¹¹ = (111³.4³)¹¹¹

Do 4 > 3 nên 111⁴ > 111³ (1)

Lại có:

3⁴ = 81

4³ = 64

Do 81 > 64 nên 3⁴ > 4³ (2)

Từ (1) và (2) ⇒ 111⁴.3⁴ > 111³.4³

⇒ (111⁴.3⁴)¹¹¹ > (111³.4³)¹¹¹

Vậy 333⁴⁴⁴ > 444³³³

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Ta có:

3^444=3^(4.111)=81^111

4^333=4^(3.111)=64^111

Do 64^111<81^111 nên 3^444>4^333

3⁴⁴⁴ = (3⁴)¹¹¹

4³³³=(4³)¹¹¹

         do 3⁴>4³

=> 3⁴⁴⁴>4³³³

333⁴⁴⁴=(3.111)^4.111=(81.111⁴)¹¹¹=(81.111.111³)¹¹¹

444³³³=(4.111)^3.111=(64.111³)¹¹¹

Vì (81.111.111³)¹¹¹>(64.111³)¹¹¹ nên 333⁴⁴⁴>444³³³

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 

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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: \(81=3^4>4^3=64\)

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

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

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

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

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

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 

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

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

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 \(333^{444}>444^{333}\)