Question

So sánh    a) 2³³³ và 3^{222       b)} 3²⁰⁰⁹ và 9¹⁰⁰⁵     c) 90²⁰ và 9999¹⁰

 

Answer 1

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

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

Có: \(8^{111}< 9^{111}\)

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

Answer 2

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

Có: \(3^{2010}>3^{2009}\)

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

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

Có: \(8100^{10}< 9999^{10}\)

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

Answer 3

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

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

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