Ta có: 333⁴⁴⁴=333^111.4=333⁴mũ 111=12296370321¹¹¹

              444³³³=444^111.3=444³mũ 111=87528384¹¹¹

Mà: 12296370321>87528384 và 111=111.

=>333⁴⁴⁴>444³³³.

Tk phát nhé

333^444 = (333^4)^111

444^333 = (444^3)^111

333^4 = 3^4.111^4 = 81.111^4

444^3 = 4^3.111^3 = 64.111^3 < 81.111^4

444^3< 333^4

(333^4)^111 > (444^3)^111

333^444 > 444^333

\(333^{444}=\left(333\times4\right)^{111}=1332^{111}\)

\(444^{333}=\left(444\times3\right)^{111}=1332^{111}\)

\(1332^{111}=1332^{111}\Rightarrow333^{444}=444^{333}\)

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

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

\(\Rightarrow333^4=111^4.3^4=111^3.111.3^4\)

     \(444^3=111^3.4^3\)

\(\Rightarrow111.3^4=111.81>4^3=64\)

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

C = 2³³³ = (2³)¹¹¹ = 8¹¹¹

D = 3²²² = (3²)¹¹¹ = 9¹¹¹

Vì  8¹¹¹ < 9¹¹¹

Nên : C < D 

1) A=333⁴⁴⁴ và B=444³³³

Ta có 333⁴⁴⁴=(3.111)^4.111=3^4.111.111^4.111=(3⁴.111⁴)¹¹¹=(81.111⁴)¹¹¹

444³³³=(4.111)^3.111=4^3.111.111^3.111=(4³.111³)¹¹¹=(64.111³)¹¹¹

Vì (81.111⁴)¹¹¹> (64.111³)¹¹¹

Nên 333⁴⁴⁴ > 444³³³

2) C=2³³³ và D=333²²²

Ta có 2³³³=2^3.111=(2³)¹¹¹=8¹¹¹

3²²²=3^2.111=(3²)¹¹¹=9¹¹¹

Vì 8¹¹¹ <9¹¹¹

Nên 2³³³< 3²²²

A=333^444

A=(333^4)^111

A=1332^111

B=444^333

B=(444^3)^111

B=1332^111

Vì 1332^111=1332^111

Nên => A=B

333^444=333^(4.111)=(333^4)^111

444^333=444^(3.111)=(444^3)^111

So sánh 333^4 với 444^3:

333^4=(111.3)^4=111^4.3^4=111^4.81

444^3=(111.4)^3=111^3.4^3=111^3.64

Vì 111^4.81>111^3.64 => 333^4>444^3 => A>B.

\(A=333^{444}=\left(3.111\right)^{444}=3^{444}.111^{444}=\left(3^4\right)^{111}.111^{444}=81^{111}.111^{444}\)

\(B=444^{333}=\left(4.111\right)^{333}=4^{333}.111^{333}=\left(4^3\right)^{111}.111^{333}=64^{111}.111^{333}\)

Vì 81¹¹¹ > 64¹¹¹ và 111⁴⁴⁴ > 111³³³

=> 81¹¹¹.111⁴⁴⁴ > 64¹¹¹.111³³³

hay 333⁴⁴⁴ > 444³³³

Vậy A > B.

A > B        

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 

BẠn vào câu hỏi tương tự 

Ta có: A=333^444=(333^4)^111

          B=444^333=(444^3)^111

A và B đã có cùng số mũ 111. Bây giờ ta so sánh 333^4 với 444^3:

333^4=(3x111)^4=3^4x111^4=81x111^4

444^3=(4x111)^3=4^3x111^3=64x111^3

Rõ ràng ta thấy 81x111^4>64x111^3 suy ra 333^4>444^3

Từ đó suy ra A>B.

Ta có:333^444=(3x111)^4x111

333^444=(3^4)^111

333^444=81^111

Ta có:444^333=(4x111)^3x111

444^333=(4^3)^111

444^333=64^111

Vì 81 > 64.Nên 81^111 > 64^111

Vậy 333^444 > 444^333. 

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

            \(444^{333}=444^{3.111}=\left(444^3\right)^{111}\)

        Ta lại có:\(333^4=\left(3.111\right)^4=81.111^4\left(1\right)\)

                        \(444^3=\left(4.111\right)^3=64.111^3\left(2\right)\)

        Từ (1) và (2)=>\(333^4>444^3hay333^{444}>444^{333}\)

333^444 > 444^333

=> A>B

Câu 2:

5^300 và 3^453

5^300 = (5^2)^150 = 25^150

3^453 > 3^450 = (3^3)^150 = 27^150

25^150 < 27^150

Vậy 5^300 < 3^453

Câu 3:

333^444 = (333^4)^111

444^333 = (444^3)^111

333^4 = 3^4.111^4 = 81.111^4

444^3 = 4^3.111^3 = 64.111^3 < 81.111^4

444^3< 333^4

(333^4)^111 > (444^3)^111

333^444 > 444^333