3²ⁿ và 2³ⁿ 

Có: 3²ⁿ = (3²)ⁿ = 9ⁿ

      2³ⁿ = (2³)ⁿ = 8ⁿ

Vì 9ⁿ > 8ⁿ nên  3²ⁿ > 2³ⁿ

a) \(27^{15}=\left(3^3\right)^{15}=3^{45}\)

\(81^{11}=\left(3^4\right)^{11}=3^{44}\)

vì 3⁴⁴ < 3⁴⁵ nên 81¹¹ < 27¹⁵

27¹⁵ = (3³)¹⁵ = 3⁴⁵

81¹¹ = (3⁴)¹¹ = 3⁴⁴

Vì 3⁴⁵ > 3⁴⁴ nên 27¹⁵ > 81¹¹

ngày mai mình trả lời cho . bận làm bài tập về nhà

777³³³<333⁷⁷⁷

777^333>333^777

k nha!

\(777^{333}=\left(777^3\right)^{111}=469097433^{111}\)

\(333^{777}=\left(333^7\right)^{111}=4,540...^{111}\)

\(\Rightarrow777^{333}>333^{777}\)

Edogawa conan

8⁶⁰³³ > 3¹⁰⁰⁵⁵

\(8^{6033}>3^{10055}\)

8⁶⁰³³ < 3¹⁰⁰⁵⁵

Học tốt !

8^6033>36=^10055hơn nha edokawa conan

3¹⁰⁰⁵⁵ < 4¹⁰⁰⁵⁵  = 2¹⁸⁰⁹⁹

8⁶⁰³³  = 2²⁰¹¹⁰

Vì 2¹⁸⁰⁹⁹   < 2²⁰¹¹⁰ => 3¹⁰⁰⁵⁵  < 8⁶⁰³³

a/ 777³³³ = [(7 . 111)³]¹¹¹ = (7³ . 111³)¹¹¹

333⁷⁷⁷ = [(3 . 111)⁷]¹¹¹ = (3⁷ . 111⁷)¹¹¹

Do: 3⁷ > 7³ ; 111⁷ > 111³   => (3⁷ . 111⁷)¹¹¹ > (7³ . 111³)¹¹¹

=> 333⁷⁷⁷ > 777³³³

Ko biết

có \(777^{333}=\left(7.111\right)^{333}=7^{333}.111^{333}=7^{3.111}.111^{333}=\left(7^3\right)^{111}.111^{333}=343^{111}.111^{333}\)

mà \(333^{777}=\left(3.111\right)^{777}=3^{777}.111^{777}=\left(3^7\right)^{111}.111^{777}=2187^{111}.111^{777}\)

ta thấy \(343^{111}< 2187^{111},111^{333}< 111^{777}\)

=> \(343^{111}.111^{333}< 2187^{111}.111^{777}\)=> \(333^{777}< 777^{333}\)

vậy...