Ta có:2³³²<2³³³= (2³)¹¹¹ =8¹¹¹

           3²²³>3²²²= (3²)¹¹¹ =9¹¹¹

Vì 8¹¹¹<9¹¹¹nên

2³³²<8¹¹¹<9¹¹¹<3²²³   => 2³³²< 3²²³

Vậy 2³³²< 3²²³ .

>

2³³² > 2²²³

Vì 332>223 nên :

=>\(2^{332}>2^{223}\)

2³³²< 2³³³=(2³)¹¹¹=8¹¹¹

3²²³>3²²²=(3²)¹¹¹=9¹¹¹

mà 8<9

=> 2³³²<3²²³

2^332 < 2^333 =  (2^3)^111 = 8^111 < 9^111 = (3^2)^111 = 3^222 < 3^223

Có : 3²²³>3²²²=(3²)¹¹¹=9¹¹¹(1)

2³³²<2³³³=(2³)¹¹¹=8¹¹¹(2)

Từ (1);(2)

=> 3²²³>2³³²

Vì:

\(3^{223}>3^{222}=\left(3^2\right)^{111}=9^{111}\)

\(2^{332}< 2^{333}=\left(2^3\right)^{111}=8^{111}\)

\(\Rightarrow3^{223}>2^{332}\)

Có 3^223 >3^222=(3^2)^111=9^111

2^332<2^333=(2^3)^111=8^111

mà 9^111 > 8^111

suy ra 3^223 >2^332

Dấu ^ la luy thừa nha

2³³²=(2³)¹¹⁰x2²=8¹¹⁰x4

3²²³=(3²)¹¹⁰x3³=9¹¹⁰x27

Vì 9¹¹⁰x27 > 8¹¹⁰x4 =>2³³² < 3²²³

có thì giải làm gì mất công hả