Question

So sánh : \(\frac{2^{2015}}{2^{2018}}\) và \(\frac{2^{2019}}{2^{2010}.256}\)

Answer 1

\(=\frac{2^{2019}}{2^{2010}.2^8}=\frac{2^{2019}}{2^{2018}}\)

vì \(2^{2019}>2^{2015}\)

\(=>\frac{2^{2019}}{2^{2018}}>\frac{2^{2015}}{2^{2018}}\)

Vậy \(\frac{2^{2019}}{2^{2010}.256}>\frac{2^{2015}}{2^{2018}}\)

Answer 2

Ta có: 

\(\frac{2^{2019}}{2^{2010}\cdot256}=\frac{2^{2019}}{2^{2010}\cdot2^8}=\frac{2^{2019}}{2^{2018}}=\frac{2}{1}=2>1\)

\(\frac{2^{2015}}{2^{2018}}=\frac{1}{2^3}=\frac{1}{8}< 1\)

\(\Rightarrow\frac{2^{2015}}{2^{2018}}< \frac{2^{2019}}{2^{2010}\cdot256}\)