a) \(21^{15}=3^{15}\cdot7^{15}\)

\(27^5\cdot49^8=\left(3^3\right)^5\cdot\left(7^2\right)^8=3^{15}\cdot7^{16}\)

vì \(7^{15}< 7^{16}\)

Nên \(3^{15}\cdot7^{15}< 3^{15}\cdot7^{16}\)

Vậy \(21^5< 27^5\cdot49^8\)

b) \(100^{45}-100^{44}=100\cdot100^{44}-100\cdot100^{43}\)

\(=100\left(100^{44}-100^{43}\right)\)

Do đó:\(100\left(100^{44}-100^{43}\right)>100^{44}-100^{43}\)

Vậy \(100^{45}-100^{44}>100^{44}-100^{43}\)

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

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

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

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

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:

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

Bạn vào câu hỏi tương tự ý có câu giống câu bạn đó !

\(72^{45}-72^{44}=72^{44}.7-72^{44}.1=72^{44}\left(7-1\right)=72^{44}.6\)

\(72^{44}-72^{43}=72^{43}.7-72^{43}.1=72^{43}\left(7-1\right)=72^{43}.6\)

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

72⁴⁵-72⁴⁴=72⁴⁴.72¹-72⁴⁴.1=72⁴⁴.(72¹-1)=72⁴⁴.71

72⁴⁴-72⁴³=72⁴³.72¹-72⁴³.1=72⁴³.(72¹-1)=72⁴³.71

vì 72⁴⁴.71<72⁴³.71

nên 72⁴⁵-72⁴⁴<72⁴⁴-72⁴³

k cho mình nha

Câu 1:

199^20 và 2003^15

199^20 = 199^15.199^5 < 199^15.1000^5 = 199^15.10^15 < 1990^15<2003^15

Vậy 199^20 < 2003^15

Câu 2:

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