\(2^{333}=\left(2^3\right)^{111}=8^{111}\\ 3^{222}=\left(3^2\right)^{111}=9^{111}\)

VÌ\(8^{111}< 9^{111}\Rightarrow2^{333}< 3^{222}\)

\(2^{333}=8^{111}< 9^{111}=3^{222}\)

`@` `\text {Ans}`

`\downarrow`

Ta có:

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

\(11^{222}=\left(11^2\right)^{111}=121^{111}\)

Vì `125 > 121 =>`\(125^{111}>121^{111}\)

`=>`\(5^{333}>11^{222}\)

Vậy, \(5^{333}>11^{222}\)

_____

`@` So sánh lũy thừa cùng cơ số:

Nếu `m > n =>`\(a^m>a^n\left(m,n\ne0,a>1\right)\)

`@` So sánh lũy thừa cùng số mũ:

Nếu `a > b =>`\(a^m>b^m\left(a,b>1,m\ne0\right)\)

`@` `\text {Kaizuu lv uuu}`

ta có: 2³³³ = (2³)¹¹¹ = 8¹¹¹

3²²² =(3²)¹¹¹ = 9¹¹¹

=> ....

TC \(2^{333}=\)\(2^{3.111}\)\(\left(2^3\right)^{111}=8^{111}\)

LC \(3^{222}=3^{2.111}=\left(3^2\right)^{111}=9^{111}\)

MÀ 8<9

\(\Rightarrow8^{111}< 9^{111}\)

\(hay\)\(2^{333}< 3^{222}\)

có ghi lộn đề không vậy:2³³³ và 3²²²

2³³² < 2³³³ = (2³)¹¹¹ = 8¹¹¹ hay 2³³² < 8¹¹¹

3²²³ > 3²²² = (3²)¹¹¹ = 9¹¹¹ hay 3²²³ > 9¹¹¹

Mà 8¹¹¹ < 9¹¹¹

=> 2³³² < 8¹¹¹ < 9¹¹¹ < 3²²³

Vậy 2³³² < 3²²³.

222^3=10941048>333222

222^3<222^333

=>222^333>3332222

\(3^{222}=9^{111};2^{333}=8^{111}\Rightarrow9^{111}>8^{111} \)

=> 3^222 > 2^333

1.

M = 2²⁰¹⁰ - ( 2²⁰⁰⁹ + 2²⁰⁰⁸ + ... + 2¹ + 2⁰ )

đặt N = 2²⁰⁰⁹ + 2²⁰⁰⁸ + ... + 2¹ + 2⁰

2N = 2²⁰¹⁰ + 2²⁰⁰⁹ + ... + 2² + 2¹

2N - N = ( 2²⁰¹⁰ + 2²⁰⁰⁹ + ... + 2² + 2¹ ) - ( 2²⁰⁰⁹ + 2²⁰⁰⁸ + ... + 2¹ + 2⁰ )

N = 2²⁰¹⁰ - 2⁰

Thay N vào ta được : 

M = 2²⁰¹⁰ - ( 2²⁰¹⁰ - 2⁰ )

M = 2²⁰¹⁰ - 2²⁰¹⁰ + 2⁰

M = 2⁰ = 1

2.

Ta có :

2³³² < 2³³³ = ( 2³ ) ¹¹¹ = 8¹¹¹

3²²³ > 3²²² = ( 3² ) ¹¹¹ = 9¹¹¹

Vì 2³³² < 8¹¹¹ < 9¹¹¹ < 3²²³

giúp mình nha 

-Vì (1/222)^333=(1/222)^3.111=(3/666)^111

     (1/333)^222=(1/333)^2.111=(2/666)^111

-Vì 111=111 và 3/666>2/666

=))(1/222)^333>(1/333)^222