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

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< 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 \(5^{35}\)

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

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 .

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