a/ \(27^{11}=\left(3^3\right)^{11}=3^{33}\); \(81^8=\left(3^4\right)^8=3^{32}< 3^{33}\Rightarrow81^8< 27^{11}\)

b/ \(3^{2n}=\left(3^2\right)^n=9^n\); \(2^{3n}=\left(2^3\right)^n=8^n< 9^n\Rightarrow2^{3n}< 3^{2n}\)

a. 27¹¹= (3³)¹¹ = 3³³

    81⁸ = (3⁴)⁸ = 3³²

Suy ra 3³³>3³² hay 27¹¹>81⁸

b. 3²ⁿ = (3²)ⁿ = 9ⁿ

     2³ⁿ = (2³)ⁿ = 8ⁿ

Mà 9>8 suy ra 9ⁿ>8ⁿ hay 3²ⁿ>2³ⁿ

c. 5²³ = 5²² . 5

   (6.5)²² = 6²² . 5²²

Vì 6²²>5 suy ra 5²² . 5<6²² . 5²² hay 5²³<(6.5)²²

d. 72⁴⁵-72⁴⁴ = 72⁴⁴(72-1) = 72⁴⁴ . 71

    72⁴⁴-72⁴³ = 72⁴³(72-1) = 72⁴³ . 71

Vì 72⁴⁴>72⁴³ suy ra 72⁴⁴ . 71>72⁴³ . 71 hay 72⁴⁵-72⁴⁴>72⁴⁴-72⁴³

a​)Ta có: 27¹¹=(3³)¹¹=3³³

              81⁸=(3⁴)⁸​=3³²

​vậy 81⁸<27¹¹

BĂNG NHAU

Ta có:

72⁴⁵ - 72⁴⁴ = 72⁴⁴.(72 - 1) = 72⁴⁴.71

72⁴⁴ - 72⁴³ = 72⁴³.(72 - 1) = 72⁴³.71

Vì 72⁴⁴.71 > 72⁴³.71

=> 72⁴⁵ - 72⁴⁴ > 72⁴⁴ - 72⁴³

Ta có:

\(72^{45}-72^{44}=72^{44}\left(72-1\right)=72^{44}.71\)

\(72^{44}-72^{43}=72^{43}\left(72-1\right)=72^{43}.71\)

Vì \(72^{44}.71>72^{43}.71\) nên \(72^{45}-72^{44}>72^{44}-72^{43}\)

bằng nhau

So sánh : và \(72^{44}-72^{43}\)

Ta có :

       \(72^{45}-72^{44}=72^{44}\left(72-1\right)\)

       \(72^{44}-72^{43}=72^{43}\left(72-1\right)\)

Vì 72⁴⁴ > 72⁴³ => 72⁴⁴ (72-1)  > 72⁴³ (72-1)

                    hay 72⁴⁵ -72⁴⁴ > 72⁴⁴ - 72⁴³ 

Nhanh hộ mọi người😦😦😦😦😦😨

\(72^{45}-72^{44}=72^{44}.\left(72-1\right)=72^{44}.71\)

\(72^{44}-72^{43}=72^{43}.\left(72-1\right)=72^{43}.71\)

Vì \(72^{44}>72^{41}\Rightarrow72^{44}.71>72^{43}.71\Rightarrow72^{45}-72^{44}>72^{44}-72^{43}\)

Theo đề bài ta có:

72⁴⁵ - 72⁴⁴ = 72⁴⁴ x ( 72 - 1 ) = 72⁴⁴ x 71

72⁴⁴ - 72⁴³ = 72⁴³ x ( 72 - 1 ) = 72⁴³ x 71

Mà 72⁴⁴ > 72⁴³ ; 71 = 71

=> 72⁴⁵ - 72⁴⁴ > 72⁴⁴ - 72⁴³ 

Lê Quang Phúc tại sao lại lấy 72-1

b1:4^10.8^15 = (2^2)^10.(2^3)^15 = 2^20.2^45 = 2^65

Không có đề bài !

đề bài đâu

78¹² - 78¹¹ =78.78¹¹ -78¹¹ =78¹¹(78-1) = 78¹¹.77

và 78¹¹ - 78¹⁰= 78.78¹⁰ -78¹⁰ =78¹⁰(78-1) = 78¹⁰.77

 ta thấy : 78¹¹.77 > 78¹⁰.77 ( vì 78¹¹ > 78¹⁰)

Suy ra: 78¹² - 78¹¹ > 78¹¹ - 78¹⁰