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

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

Vì \(8^{111}< 9^{111}\) mà \(2^{332}< 8^{111},3^{223}>9^{111}\) nên suy ra \(2^{332}< 3^{223}\)

Vậy \(2^{332}< 3^{223}\)

1) \(A=\dfrac{10^{2013}+1}{10^{2014}+1}\Rightarrow10A=\dfrac{10^{2014}+10}{10^{2014}+1}=\dfrac{10^{2014}+1}{10^{2014}+1}+\dfrac{9}{10^{2014}+1}=1+\dfrac{9}{10^{2014}+1}\)

\(B=\dfrac{10^{2014}+1}{10^{2015}+1}\Rightarrow10B=\dfrac{10^{2015}+10}{10^{2015}+1}=\dfrac{10^{2015}+1}{10^{2015}+1}+\dfrac{9}{10^{2015}+1}=1+\dfrac{9}{10^{2015}+1}\)Vì: \(10^{2014}+1< 10^{2015}+1\Rightarrow\dfrac{9}{10^{2014}+1}>\dfrac{9}{10^{2015}+1}\Rightarrow1+\dfrac{9}{10^{2014}+1}>1+\dfrac{9}{10^{2015}+1}\)

Nên suy ra \(10A>10B\Rightarrow A>B\)

Ta có:\(2^{332}<2^{333}=2^{3.111}=\left(2^3\right)^{111}=8^{111}\)

        \(3^{223}>3^{222}=3^{2.111}=\left(3^2\right)^{111}=9^{111}\)

Vì \(8^{111}<9^{111}\)nên \(2^{333}<3^{222}nên2^{332}<3^{223}\)

dap an A>B ung ho mk nhe

>

2³³² > 2²²³

Vì 332>223 nên :

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

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

a) 3⁴⁰⁰ =3^2.200 =9²⁰⁰  vậy 3⁴⁰⁰ = 9²⁰⁰

b) 2³³² < 2³³³ mà 2³³³ = 2^3.111 = 8¹¹¹

   3²³³ > 3²²² mà 3²²² = 3^2.111 = 9¹¹¹

mà 8 < 9

=> 2³³² < 3²²³

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