Question

so sánh ; \(2009^{20}và20092009^{10}\)

Answer 1

ta có

2009²⁰ = (2009 2 )¹⁰= (2009.2009)¹⁰

20092009¹⁰ = (2009.10 001)¹⁰

Vì 2009.2009 < 2009. 10 001 nên 2009²⁰ < 20092009¹⁰

Answer 2

Ta có :

\(2009^{20}=\left(2009^2\right)^{10}\\ 20092009^{10}=\left(2009\cdot10001\right)^{10}.\\ Vì2009^2=2009\cdot2009< 2009\cdot10001nên:\\ 2009^{20}< 20092009^{10}\)

Vậy \(2009^{20}< 20092009^{10}\)