Find the largest value of power.
Golfscript - 26 chars

~:x,{:b;x,{b?x=b*}%+}*$-1&gt;


Rough translation to Python

x=input()
acc = []
for b in range(x):
    for _ in range(x):
        acc.append((_**b==x)*b) # most of these are zeros
print max(acc)


So it loops way more times that necessary, but that often happens with golfed answers