Why is Math.pow(0, 0) === 1?

Question

We all know that 0⁰ is indeterminate.

But, javascript says that:

Math.pow(0, 0) === 1 // true

Answer 1

For this to understand you need to solve calculus:

Expanding x^x around zero using Taylor series, we get:

So to understand what's going on with limit when x goes to zero, we need to find out what's going on with second term x log(x), because other terms are proportional to x log(x) raised to some power.

We need to use transformation:

Now after this transformation we can use L'Hôpital's rule, which states that:

So differentiating that transformation we get:

So we've calculated that term log(x)*x approaches 0 when x approaches 0. It's easy to see that other consecutive terms also approaches zero and even faster than second term.

So at point x=0, series becomes 1 + 0 + 0 + 0 + ... and thus equals to 1.