Suppose pi = 3.14nnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnn.
That is, pi = 3.14n48.
We want to solve for n. (Yes, we really do.)
Dividing both sides by 3.14 yields
pi/3.14 = n48.
Then, taking the 48th root of each side yields
(pi/3.14)1/48 = (n48)1/48
(since, in general, the mth root of x is given by x1/m).
(pi/3.14)1/48 = n
(since, in general, (yz)1/z = y).