\(27^{13}=\left(3^3\right)^{13}=3^{39};243^8=\left(3^5\right)^8=3^{40};3^{39}< 3^{40}\Rightarrow27^{13}< 243^8\\ 125^{80}=\left(5^3\right)^{80}=5^{240};25^{118}=\left(5^2\right)^{118}=5^{236};5^{240}>5^{236}\Rightarrow125^{80}>25^{118}\)

\(27^{13}< 243^8;125^{80}>25^{118}\)

\(125^{80}=\left(5^3\right)^{80}=5^{240}\\ 25^{118}=\left(5^2\right)^{118}=5^{236}\)

Vì \(5^{240}>5^{236}\)nên \(125^{80}>25^{118}\)

a. \(5^{127}=5.5^{126}=5.125^{72}>119^{72}\)

\(\Rightarrow5^{217}>119^{72}\)

b. \(2^{1000}=\left(2^5\right)^{200}=32^{200}\)

\(5^{400}=\left(5^2\right)^{200}=25^{200}\)

\(\Rightarrow2^{1000}>5^{400}\)

c. \(9^{12}=\left(3^2\right)^{12}=3^{24}\)

\(27^7=\left(3^3\right)^7=3^{21}\)

\(\Rightarrow9^{12}>27^7\)

d. \(125^{80}=\left(5^3\right)^{80}=5^{240}\)

\(25^{118}=\left(5^2\right)^{118}=5^{236}\)

\(\Rightarrow125^{80}>25^{118}\)

e. \(5^{40}=\left(5^4\right)^{10}=625^{10}\)

\(\Rightarrow5^{40}>620^{10}\)

f. \(27^{11}=\left(3^3\right)^{11}=3^{33}\)

\(81^8=\left(3^4\right)^8=3^{32}\)

\(\Rightarrow27^{11}>81^8\)

3^(2*12) và 3^(3*7)

3^24>3^21

9¹² < 27⁷ 

vì :

9¹² < 9 ²¹ 

5³⁶ = (5³)¹² = 125¹² ; 11²⁴ = (11²)¹² = 121¹².Vì 125¹² > 121¹² nên 5³⁶ > 11²⁴

Ta có: 2¹⁶=2¹³.2³=2¹³.8

Vì 8>7 => 2¹³.8>7.2¹³ => 2¹⁶>7.2¹³

Ta có : 27^11 = (3^3)^11 = 3^33

           81^8   = (3^4)^8   = 3^32

Vì 3^33 > 3^32 nên 27^11 > 81^8

Ta có: 27¹¹=(3³)¹¹=3^3.11=3³³

         81⁸=(3⁴)⁸=3^4.8=3³²

Vì 3³²<3³³ => 81⁸<27¹¹

27^11 = (3^3 )^11 = 3^33

81^8 = (3^4)^8 =3^32

vậy 27^11 nhỏ hơn 81^8

Ta có: 5⁴⁰=5^4.10=(5⁴)¹⁰=625¹⁰

Vì 625¹⁰>620¹⁰ => 5⁴⁰ > 620¹⁰

Ta có : 5⁴⁰=5^4.10=(5⁴)¹⁰ =625¹⁰

Mà 625¹⁰ > 620¹⁰

Suy ra 5⁴⁰ > 620¹⁰

333⁴⁴⁴>444³³³

5^217=5.5^(3.72)=5.(125)^72>125^72