You can figure it out by breaking your number into two parts, x (the true value of PI), and y (the error part). y is going to be some smallish figure, expressed as, say, 1e-10, or whatever. Your problem then becomes calculating the difference between x**n, and (x+y)**n; you can estimate the error in this way. For n=2, you'd get  x**2 + 2xy + y**2. Plug in the value for y to get your error. The error would be about  6.8e-10 + 1e-20.

You might consider using fractions instead of floats. If you are able to obtain a fraction that approximates PI, you can play around with exponents more safely. Using bigint, you could do this without concern for overflow, underflow, or other problems related to floats. Just a thought.