1. 5³⁶ = (5³)¹² = 125¹²

11²⁴ = (11²)¹² = 121¹²

Vì 125 > 121 và 12 = 12 => 125¹² > 121¹² => 5³⁶ > 11²⁴

2. 3²ⁿ = (3²)ⁿ = 9ⁿ

2³ⁿ = (2³)ⁿ = 8ⁿ. Vì 9 > 8 ; n = n => 9ⁿ > 8ⁿ => 3²ⁿ > 2³ⁿ

3. 5²³ = 5.5²²

Vì 5 < 6 ; 5²² = 5²² => 5.5²² < 6.5²² =>5²³ < 6.5²²

4. Có: 2¹⁶ = 2¹³.2³ = 2¹³.8

Vì 7 < 8 => 7.2¹³ < 2¹⁶

5. 27⁵.49⁸ = 3¹⁵.7¹⁶ = 3¹⁵.7¹⁵.7 = 21¹⁵.7 > 21¹⁵ => 21¹⁵ < 27⁵.49⁸

Câu bổ sung: 72⁵⁵ - 72⁴⁴ = 72⁴⁴.(72 - 1) = 72⁴⁴.71

72⁴⁴ - 72⁴³ = 72⁴³.(72 - 1) = 72⁴³.71 < 72⁴⁴.71 => 72⁴⁵ - 72⁴⁴ > 72⁴⁴ - 72⁴³

Thanks bạn nhé!!

Ta có :

72⁴⁵ - 72⁴⁴ = 72⁴⁴ . ( 7 - 1 ) = 72⁴⁴ . 6

72⁴⁴ - 72⁴³ = 72⁴³ . ( 7 - 1 ) = 72⁴³ . 6

Vì 72⁴⁴ . 6 > 72⁴³ . 6 nên 72⁴⁵ - 72⁴⁴ > 72⁴⁴ - 72⁴³

72⁴⁵ - 72⁴⁴ 

= 72⁴⁴ .72  -  72⁴⁴

= 72⁴⁴. ( 72 - 1 ) 

72⁴⁴ - 72⁴³ 

= 72⁴³ . 72 - 72⁴³ 

= 72⁴³ . ( 72 - 1 ) 

+ ) Vì 72⁴⁴ . ( 72 -1 ) > 72⁴³ . ( 72 -  1 ) nên 72⁴⁵ - 72⁴⁴ > 72⁴⁴ - 72⁴³ 

^^ Chúc học tốt nhé!!!!

a. Ta có: \(5^{36}=\left(5^3\right)^{12}=125^{12}\)

\(11^{24}=\left(11^2\right)^{12}=121^{12}\)

\(Do\)\(125^{12}>121^{12}\Rightarrow5^{36}>11^{24}\)

b) Ta có; \(6.5^{22}>5.5^{22}=5^{23}\)

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

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

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

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

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

VÌ \(77^{44}.71>72^{43}.71\)

Nên \(72^{45}-72^{44}>72^{43}.71\)

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

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

Ta thấy: 72⁴⁴.71 > 72⁴³.71

=> \(72^{45}-72^{44}>72^{44}-72^{43}\)

Câu 1:

5^23 và 6.5^22

5^23 = 5.5^22 < 6.5^22

Vậy 5^23 < 6.5^22

Câu 2:

7.2^13 và 2^16

7.2^13 < 8.2^13 = 2^3.2^13 = 2^16

Vậy 7.2^13 < 2^16

72⁴⁵-72⁴⁴=72⁴⁴.(72-1)=72⁴⁴.71

72⁴⁴-72⁴³=72⁴³.(72-1)=72⁴³.71

Do 72⁴⁴.71>72⁴³.71

Nên 72⁴⁵-72⁴⁴>72⁴⁴-72⁴³

đặt A=72^45-72^44=72^44.(72-1)   (1)

B=72^44-72^43=72^43.(72-1)    (2)

từ 1 và 2 => A>B

Câu 1:

A = 72^45 - 72^44 = 72^44.(72 - 1) = 72^44.71

B = 72^44 - 72^43 = 72^43.(72 - 1) = 72^43.71

A > B

Câu 2:

A = 78^12 - 78^11 và B = 78^11 - 78^10

A = 78^12.(78 - 1) = 78^12.77

B = 78^11 - 78^10 = 78^10.(78 - 1) = 78^10.77

A > B