ta có\(\frac{3^7.9^{10}}{27^8}\)

= > \(\frac{3^7.9^2.9^8}{\left(3.9\right)^8}\)

=>\(\frac{3^7.9^2.9^8}{3^8.9^8}\)

=>\(\frac{3^7.9^2}{3.3^7}\)

=>

=> \(\frac{9^2}{3}\)

=> \(\frac{\left(3.3\right)^2}{3}\)

=>\(\frac{3^2.3^2}{3}\)

=\(\frac{3.3.3^2}{3}\)

= 3 . 3^2

= 3^3

= 27

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

\(2^{91}=\left(2^{13}\right)^7=73728^7\)

\(5^{35}=\left(5^5\right)^7=3125^7\) nhỏ hơn \(73728^7\)

\(\Rightarrow2^{91}\) lớn hơn \(5^{35}\)

\(b,3^{400}=\left(3^4\right)^{100}=81^{100}\\ 4^{300}=\left(4^3\right)^{100}=64^{100}\\ Vì:81^{100}>64^{100}\left(Do:81>64\right)\\ \Rightarrow3^{400}>4^{300}\)

\(d,10^{20}=\left(10^2\right)^{10}=100^{10}\\ Vì:100^{10}>20^{10}\left(Do:100>20\right)\\ \Rightarrow10^{20}>20^{10}\)

Ta có:2³³²<2³³³= (2³)¹¹¹ =8¹¹¹

           3²²³>3²²²= (3²)¹¹¹ =9¹¹¹

Vì 8¹¹¹<9¹¹¹nên

2³³²<8¹¹¹<9¹¹¹<3²²³   => 2³³²< 3²²³

Vậy 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

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