\(2^{333}< 3^{222}\)

a: \(2^{333}=8^{111}< 9^{111}=3^{222}\)

a) \(2^{333}=2^{3.111}=\left(2^3\right)^{111}=8^{111}\)

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

Vì \(8< 9\)\(\Rightarrow8^{111}< 9^{111}\)\(\Rightarrow2^{333}< 3^{222}\)

b) \(9^{1005}=\left(3^2\right)^{1005}=3^{2.1005}=3^{2010}>3^{2009}\)

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

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

Có: \(8^{111}< 9^{111}\)

\(\Leftrightarrow2^{333}< 3^{222}\)

\(9^{1005}=\left(3^2\right)^{1005}=3^{2010}\)

Có: \(3^{2010}>3^{2009}\)

\(\Rightarrow9^{1005}>3^{2009}\)

\(90^{20}=\left(90^2\right)^{10}=8100^{10}\)

Có: \(8100^{10}< 9999^{10}\)

\(\Rightarrow90^{20}< 9999^{10}\)

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

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

\(\Rightarrow2^{333}< 3^{222}\)

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

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

Do : \(8^{111}< 9^{111}\left(8< 9\right)\)

\(\Rightarrow2^{333}< 3^{222}\)

Ta có : \(9^{1005}=\left(3^2\right)^{1005}=3^{2010}\)

Do : \(3^{2009}< 3^{2010}\left(2009< 2010\right)\)

\(\Rightarrow3^{2009}< 9^{1005}\)

Ta có : \(99^{20}=\left(99^2\right)^{10}=9801^{10}\)

Do : \(9801^{10}< 9999^{10}\left(9801< 9999\right)\)

\(\Rightarrow99^{20}< 9999^{10}\)

\(A,2^{333}\) và \(3^{222}\)

Ta có:

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

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

Vì 8<9 \(\Rightarrow8^{111}< 9^{111}\)

\(\Rightarrow2^{333}< 3^{222}\)

B,\(3^{2009}\) và \(9^{2005}\)

Ta có:

\(9^{2005}=\left(3^2\right)^{2005}=3^{4010}\)

Vì 2009 < 4010 \(\Rightarrow3^{2009}< 3^{4010}\)

2³³³=(2³)¹¹¹=8¹¹¹

3²²²=(3²)¹¹¹=9¹¹¹

Vì: 8<9 nên: 8¹¹¹<9¹¹¹

vậy: 2³³³<3²²²

b, 99²⁰=(99²)¹⁰=9801¹⁰

Mà: 9801<9999 nên:

99²⁰<9999¹⁰

aTa có:

2³³³=(2³)¹¹¹=8¹¹¹

3²²²=(3²)¹¹¹=9¹¹¹

Do 8¹¹¹<9¹¹¹

=>2³³³<3²²²

b,Ta có:

99²⁰=(99²)¹⁰=9801¹⁰

Do 9801¹⁰ <9999¹⁰

=>99²⁰<9999¹⁰