Question

So sánh:

a ) 2\(^{333}\)và 3\(^{222}\)

b ) 3\(^{2009}\)và 9\(^{1005}\)

c ) 99\(^{20}\)và 9999\(^{^{10}}\)

Answer 1

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

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

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

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

Answer 2

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

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

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

Answer 3

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

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

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