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

\(8^{111}<9^{111}=\left(3^2\right)^{111}=3^{222}<3^{223}\)

Do đó: \(2^{332}<3^{223}\)

>

2³³² > 2²²³

5³³²= (5²)¹⁶⁶ =25¹⁶⁶ < 27¹⁶⁶ = (3³)¹⁶⁶ = 3⁴⁹⁸< 3⁵⁰¹

=> 5³³² < 3⁵⁰¹

    Vậy 5³³² < 3⁵⁰¹

5³³²=(5²)¹⁶⁶=25¹⁶⁶

3⁵⁰¹=(3³)¹⁶⁷=27¹⁶⁷

=>5³³²<3⁵⁰¹

2332< 2333=(23)111=8111

3223>3222=(32)111=9111

mà 8<9

=> 2332<3223

đúng tk cho mik

Ta có: 2³³² = 2³³⁰⁺² = 2³³⁰ .2² = (2³)¹¹⁰.4= 8¹¹⁰ . 4

          3²²³ = 3²²⁰⁺³ = 3²²⁰ . 3³ =(3²)¹¹⁰ . 27=9¹¹⁰ . 27

Vì 8<9 , 4<27  => 8¹¹⁰< 9¹¹⁰

                       => 8¹¹⁰ . 4 < 9¹¹⁰ . 27

                       => 2³³² < 3²²³

3³⁰⁰ > 2³⁰⁰ ( vì 3 > 2 ).

3^200 = (3^2)^100 = 9^100 

2^300 = (2^3)^100 = 8^100 

Vì 9^100 > 8^100 

Vậy 3^200 > 2^300 

a: -3/4=-9/12

-5/6=-10/12

mà -9>-10

nên -3/4>-5/6

b: -5/17<0<2/7

c: 11/10>1>9/14

Ta có:\(\frac{111}{332}\)>\(\frac{111}{333}\)=\(\frac{1}{3}\)\(\Rightarrow\)\(\frac{111}{332}\)>\(\frac{1}{3}\)

         \(\frac{166}{499}\)<\(\frac{166}{498}\)=\(\frac{1}{3}\)\(\Rightarrow\)\(\frac{166}{499}\)<\(\frac{1}{3}\)

\(\Rightarrow\)\(\frac{111}{332}\)>\(\frac{166}{499}\)

Vậy\(\frac{111}{332}\)>\(\frac{166}{499}\)

Bước 1: So sánh các lũy thừa gần nhau

• Ta có:

\(2^{332} < 2^{333} , 2^{333} = 8^{111}\) \(3^{223} > 3^{222} , 3^{222} = 9^{111}\)

Bước 2: So sánh \(8^{111}\) và \(9^{111}\)

• Rõ ràng: \(8 < 9 \textrm{ }\textrm{ } \Longrightarrow \textrm{ }\textrm{ } 8^{111} < 9^{111}\)

Bước 3: Kết hợp tất cả

\(2^{332} < 2^{333} = 8^{111} < 9^{111} = 3^{222} < 3^{223}\) \(\textrm{ }\textrm{ } \Longrightarrow \textrm{ }\textrm{ } 2^{332} < 3^{223} .\)

✅ Kết luận:

\(\boxed{2^{332} < 3^{223}}\)

Ta có:2³³²<2³³³= (2³)¹¹¹ =8¹¹¹

           3²²³>3²²²= (3²)¹¹¹ =9¹¹¹

Vì 8¹¹¹<9¹¹¹nên

2³³²<8¹¹¹<9¹¹¹<3²²³   => 2³³²< 3²²³

Vậy 2³³²< 3²²³ .