Question

So sánh:

\(3^{250}\) và \(2^{375}\)

Answer 1

\(3^{250}\) và    \(2^{375}\)

Ta có : \(3^{250}=\left(3^2\right)^{125}=9^{125}\) 

            \(2^{375}=\left(2^3\right)^{125}=8^{125}\)

Vì \(9^{125}>8^{125}\) nên       \(3^{250}>2^{375}\)

\(\Rightarrow3^{250}>2^{375}\) 

Answer 2

\(3^{250}=\left(3^2\right)^{125}=9^{125};2^{375}=\left(2^3\right)^{125}=8^{125}\)

Vì\(9^{125}>8^{125}\Rightarrow3^{250}>2^{375}\)

Answer 3

Ta có: 3²⁵⁰ = (3²)¹²⁵ = 9¹²⁵

2³⁷⁵ = (2³)¹²⁵ = 8¹²⁵

Vì 9¹²⁵ > 8¹²⁵ nên 3²⁵⁰ > 2³⁷⁵

Vậy 3²⁵⁰ > 2³⁷⁵