a) Ta có
$5^{2011} = 5^{2 + 2009} = 5^2 . 5^{2009} = 25.5^{2009}$
Ta có $25<30$ nên $25.5^{2009} < 30 . 5^{2009}$
Vậy $5^{2011} < 30 . 5^{2009}$
b) Ta có
$2010 . 2012 = (2011-1)(2011+1) = 2011.2011 + 2011 - 2011 - 1 = 2011.2011-1 < 2011.2011$.
Vậy $2010.2012 < 2011.2011$.