Lây U chung lớn nhất của các mẫu 

  199²⁰ > 2003¹⁵

  72⁴⁵ - 72⁴⁴  < 72⁴⁴ - 72⁴³

a) \(21^{15}=21^{3.5}=\left(21^3\right)^5=9261^5\)

Vì \(9261>27\Rightarrow9261^5>27^5\Rightarrow21^{15}>27^5\)

b) \(15^{12}=\left(3.5\right)^{12}=3^{12}.5^{12}\)

\(81^3.125^5=\left(3^4\right)^3.\left(5^3\right)^5=3^{4.3}.5^{3.5}=3^{12}.5^{15}\)

Vì \(3^{12}=3^{12}\)mà \(5^{12}< 5^{15}\Rightarrow3^{12}.5^{12}< 3^{12}.5^{15}\Rightarrow15^{12}< 81^3.125^5\)

a>\(16^{19}=2^{4^{19}}=2^{76}\\ 8^{25}=2^{3^{25}}=2^{75}\)

16^19>8^25

72⁴⁵-72⁴⁴=72^(45-44)=72¹=72

72⁴⁴-72⁴³=72^(44-43)=72¹=72

\(\Rightarrow\)72⁴⁵-72⁴⁴=72⁴⁴-72⁴³

\(72^{45}-72^{44}=72^{44}.72-72^{43}.72=72.\left(72^{44}-72^{43}\right)\)

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

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

\(72^{44}-72^{43}=7^{44}\left(71-1\right)=72^{44}.71\)

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

a,2003¹⁵ lớn hơn

b,11²¹ lớn hơn

c,72⁴⁵- 72⁴⁴lớnhơn