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

I'd like to disagree with some of the previous answers' assertion that it's a matter of convention or convenience (covering some special cases for various theorems, etc) that 0^0 be defined as 1 instead of 0.

Exponentiation doesn't actually fit that well with our other mathematical notations, so the definition we all learn leaves room for confusion. A slightly different way of approaching it is to say that a^b (or exp(a, b), if you like) returns the value multiplicatively equivalent to multiplying some other thing by a, repeated b times.

When we multiply 5 by 4, 2 times, we get 80. We've multiplied 5 by 16. So 4^2 = 16.

When you multiply 14 by 0, 0 times, we are left with 14. We've multiplied it 1. Hence, 0^0 = 1.

This line of thinking might also help to clarify negative and fractional exponents. 4^(-2) is a 16th, because 'negative multiplication' is division - we divide by four twice.

a^(1/2) is root(a), because multiplying something by the root of a is half the multiplicative work as multiplying it by a itself - you would have to do it twice to multiply something by 4 = 4^1 = (4^(1/2))^2