Ta co: 333⁴⁴⁴ = (3*111)^4*111

                          = (3⁴)¹¹¹

                       = 81¹¹¹

Ta co: 444³³³ = (4*111)^3*111

                      = (4³)¹¹¹

                      = 64¹¹¹

Vi 81 > 64 nen 81¹¹¹ > 64¹¹¹

Vay 333⁴⁴⁴ > 444³³³

^{HAY THI NHE}

Ta có:333⁴⁴⁴ = (333⁴)¹¹¹

            444³³³ =(444³)¹¹¹

Ta so sánh 333⁴ và 444³

333⁴ =(3.111)⁴ =3⁴. 111⁴ =81.111⁴

444³ =(4.111)³ =4³.111³ = 64.111³

Ta thấy 81>64 và 111⁴>111³

=>333⁴>444³ do đó: 333⁴>444³

Ta có:

 333^ 444 = (3.111) ^ (4.111)

               = 3^(4.111) . 111^(4.111)

              = (3^4)^111 . 111 ^444 = 81^111 . 111^444

444^333 = (4.111) ^  (3.111)

             = 4 ^ (3.111) . 111^(3.111)

             = ( 4^3)^111 . 111^333 = 64^111 . 111^333

Vì 81^111 > 64^111 ; 111^444 > 111^333

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

Vậy 333^444 > 444^333

\(\left(-333\right)^{444}=3^{444}=\left(3^4\right)^{111}=81^{111}\)

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

\(81^{111}>64^{111}\Rightarrow\left(-3\right)^{444}>444^{333}\)

a) 333⁴⁴⁴ và 444³³³

Ta có :

333⁴⁴⁴ = (111 . 3)⁴⁴⁴ = 111⁴⁴⁴ . 3⁴⁴⁴ = 111³³³ . 111¹¹¹ . 3⁴⁴⁴

444³³³ = (111 . 4)³³³ = 111³³³ . 4³³³

Giờ, ta chỉ cần so sánh 111¹¹¹ . 3⁴⁴⁴ và 4³³³

Ta có :

4³³³ = 4¹¹¹ . 4¹¹¹ . 4¹¹¹ = (4 . 4 . 4)¹¹¹ = 64¹¹¹

Vì 64¹¹¹ < 111¹¹¹ nên 111¹¹¹ . 3⁴⁴⁴ > 4³³³

=> 111³³³ . 111¹¹¹ . 3⁴⁴⁴ > 111³³³ . 4³³³

=> 333⁴⁴⁴ > 444³³³

b) A = 2012 . 20112011 và B = 2011 . 20122012

A = 2012 . 20112011 = 2011 . 20112011 + 20112011

B = 2011 . 20122012 => B = 2011 . 20112011 + 2011 . 10001 = 2011 . 20112011 + 2011 . 10001 = 2011 . 20112011 + 20112011

Vì 2011 . 20112011 + 20112011 = 2011 . 20112011 + 20112011 nên A = B = 2011 . 20112011 + 20112011

CHÚC BẠN HỌC TỐT NHA

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: \(81=3^4>4^3=64\)

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

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

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

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

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

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 \(333^{444}>444^{333}\)

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