Question

So sánh:

a. \(2^{333}\)và \(3^{222}\)

b. \(3^{2009}\)và \(9^{1005}\)

c. \(99^{20}\)và \(9999^{10}\)

Answer 1

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

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

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

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

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

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

Vì \(9801^{10}< 9999^{10}\Rightarrow99^{20}< 9999^{10}\)

Answer 2

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

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

Vì 9>8 nên 9¹¹¹>8¹¹¹

Vậy 3²²²>2³³³

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

Vì 2010>2009 nên 3²⁰¹⁰>3²⁰⁰⁹

Vậy 9¹⁰⁰⁵>3²⁰⁰⁹

c)Ta có:\(99^{20}=\left(99^2\right)^{10}=\left(99.99\right)^{10}\)

\(9999^{10}=\left(99.101\right)^{10}\)

Vì 99<101 nên (99.99)¹⁰<(99.101)¹⁰

Vậy 99²⁰<9999¹⁰