ta có

9^1005=(3^2)^1005

          =3^2010

vi 3^2010>3^2009

=>3^2009<9^1005

Ta có :

9^1005 = ( 3^2 ) ^ 1005 = 3^2010

Vì 3^2009 < 3^2010

=> 3^2009 < 9^1005

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

a.ta có: \(3^{2009}\)

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

*Vì 2010> 2009 =>\(3^{2009}\) < \(3^{2010}\)

Vậy \(3^{2009}\) < \(9^{1005}\).

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

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

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

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:

9¹⁰⁰⁵ = (3²)¹⁰⁰⁵ = 3²⁰¹⁰

Mà 3²⁰¹⁰ > 3²⁰⁰⁹ ( 2010 > 2009 )

=> 9¹⁰⁰⁵ > 3²⁰⁰⁹

Ta có :

\(3^{2009}\left(1\right)\)

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

Từ \(\left(1\right)+\left(2\right)\Leftrightarrow3^{2009}< 3^{1005}\)

Ta có: \(3^{2009}\) ( giữ nguyên )

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

Vì 2009 < 2010 nên \(3^{2009}< 3^{2010}\)

Vậy \(3^{2009}\) < \(9^{1005}\)

ta có 9¹⁰⁰⁵=(3²)¹⁰⁰⁵=3²⁰¹⁰

vì 2009<2010

=> 3²⁰⁰⁹< 3²⁰¹⁰

hay 3²⁰⁰⁹ <9¹⁰⁰⁵

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

Vì : 2009 < 2010 nên \(3^{2009< }3^{2010}\)

Vậy \(3^{2009}< 9^{1005}\)