## What is 0 to the Power of 0?

We know that a nonzero number to the power of zero is one and zero to the power of a nonzero number is zero. So what is zero to the power of zero? Is it One? Zero? Undefined? It turns out that there is no single accepted answer–and this illustrates that mathematical definitions are not objective.

We know that a nonzero number to the power of zero is one and zero to the power of a nonzero number is zero. So what is zero to the power of zero? Is it One? Zero? Undefined? It turns out that there is no single accepted answer — and this illustrates that mathematical definitions are not objective. We know that a3 is equal to a multiplied by itself 3 times, or a•a•a. Then, 03 is 0 multiplied by itself 3, which is still 0. That gives us the pattern: This suggests that 00 = 0, but it is not the...