555³³³ = (555³)¹¹¹ 

333⁵⁵⁵ = (333⁵)¹¹¹

vì mũ của hai số giống nhau nên ta đi so sánh 555³ và 333⁵

555³ = (5 . 111)³ = 5³ . 111³ = 125 . 111³

333⁵ = (3 . 111)⁵ = 3⁵ . 111⁵ = 243 . 111⁵

Vì 125 . 111³ < 243 . 111⁵ nên 333⁵ < 555³

hay 555³³³ < 333⁵⁵⁵

vậy 555³³³ < 333⁵⁵⁵

555^333<333^555

Ta có: \(333^{555}=\left(3.111\right)^{555}=3^{555}.111^{555}=\left(3^5\right)^{111}.111^5=243^{111}.111^5\)

          \(555^{333}=\left(5.111\right)^{333}=5^{333}.111^{333}=\left(5^3\right)^{111}.111^{555}=125^{111}.111^{555}\)

Vì \(243^{111}.111^{555}>125^{111}.111^3\) nên \(333^{555}>555^{333}\)

>             

sao trúc làm lộn tùng phèo vậy

tự dưng đang 111³³³ biến thành 111⁵⁵⁵

vfyhgjn

Ta có: \(333^{555}=\left(3.111\right)^{555}=3^{555}.111^{555}=\left(3^5\right)^{111}.111^{555}=243^{111}.111^{555}\)

\(555^{333}=\left(5.111\right)^{333}=5^{333}.111^{333}=\left(5^3\right)^{111}.111^{333}=125^{111}.111^{333}\)

Vì \(125^{111}< 243^{111}\)và \(111^{333}< 111^{555}\)

\(\Rightarrow125^{111}.111^{333}< 243^{111}.111^{555}\)

Vậy \(555^{333}< 333^{555}\)

A=\(333^{555} = (333^5)^{111} = (( 111 . 3 )^5 ) ^{111} =( 111^5 . 3^5 )^{111} \)

B=\(555^{333}= ( 555^3) ^{111} =(( 111.5 ) ^3 )^{111} = (111^3 . 5^3 )^{111} \)

Ta thấy \(111^5 > 111^3 \)  và \(3^5(243)>5^3 (125)\)

=> A>B

333⁵⁵⁵=(3.111)^5.111=(243.111⁵)¹¹¹=(243.111.111.111³)¹¹¹

555³³³=(5.111)^3.111=(125.111³)¹¹¹

=>333⁵⁵⁵>555³³³

tick mk nha

DẤU NÀY > NHA BẠN.

333^{555 và} 555³³³

= 333⁵⁵⁵ = ( 3.111 )⁵⁵⁵ = 3⁵⁵⁵ . 111⁵⁵⁵ = ( 4⁵ )¹¹¹ . 111⁵⁵⁵ = 1024¹¹¹ . 111⁵⁵⁵

= 555³³³ = ( 5.111 )³³³ = 5³³³ . 111³³³  = ( 5³ )¹¹¹ . 111³³³ = 125¹¹¹ . 111³³³

 Vì 1024¹¹¹ . 111⁵⁵⁵ > 125¹¹¹ . 111³³³

\(\Rightarrow\)3⁵⁵⁵ > 555³³³

Đặt 333⁵⁵⁵ =A ; 555³³³ =B Ta có:

A=333⁵⁵⁵ =(3.111)^5.111 =3^5.111  .111^5.111

B=555³³³ = (5.111)^3.111 = 5^3.111  .111^3.111

Vậy.........

(333^2)555                    (555^2)^333

110889^555           <        308025^333

Vậy: 333^555<555^333

A = 333⁵⁵⁵ = (3.111)⁵⁵⁵ = 3⁵⁵⁵.111⁵⁵⁵ = (3⁵)¹¹¹.111⁵⁵⁵ = 243¹¹¹.111⁵⁵⁵

555³³³ = (5.111)³³³ = 5³³³.111³³³ = (5³)¹¹¹.111³³³ = 125¹¹¹.111³³³

Vì 243¹¹¹.111⁵⁵⁵ > 125¹¹¹.111³³³

=> 333⁵⁵⁵ > 555³³³

hay A > B

\(vi333^{555}>555^{333}nenA>B\)

chuc bn hoc gioi!

nhae

bn

$$$

(______^______^_______)

333⁵⁵⁵ và 555³³³

333⁵⁵⁵ = 333^100.5 = ( 333⁵)¹⁰⁰ = 4094691316893¹⁰⁰

555³³³ = 555^100.3 =( 555³)¹⁰⁰ = 170953875¹⁰⁰

Vì 4094691316893¹⁰⁰>170953875¹⁰⁰

Nên 333⁵⁵⁵>555³³³ 

\(333^{333}=3^{333}.111^{333}\)

\(555^{222}=5^{222}.111^2\)

\(3^{333}=27^{111}>5^{222}=25^{111}\) (1)

\(111^{333}>111^{222}\)(2)

Từ (1) và (2) \(\rightarrow333^{333}>555^{222}\)