Question

[Võ Thiên Hương]

So sánh:

a) \(2^{333}\)và \(3^{222}\)

b) \(3^{2009}\)và \(9^{1005}\)

c) \(99^{20}\) và \(9999^{10}\)

Answer 1

[Chu Công Đức]

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