Mathematica interprets numbers entered as decimals as machine precision. The easiest but not only way to get a high precision answer to your problem is to enter a rational: N[(5/2)^125,30].
On Sunday, February 17, 2013, Blaise F Egan wrote:
> I am trying to evaluate 2.5^125 to high precision. > > R gives 5.527147875260445183346e+49 as the answer but Mathematica with > N[2.5^125,30] gives 5.52715*10^49 and says that is to machine precision. > > I am inexperienced at Mathematica. Am I doing something silly? > > Blaise > >