Why is X raised to the power of 0 = 1?

Question

So as the topic states, why is 5^0 = 1 and not 5 or 0? Is it only because the other exponential laws wouldn't work if it was not the case?

Answer 1

$5^0$ is the product of zero $5$s, which is the empty product, and there are plenty of reasons to define that as $1$.

Answer 2

This convention allows us to use the additive property of exponents: $b^xb^y = b^{x+y}$ without having to define an edge case for $0$. Example:

$$2^4 = 16 \\ 2^{-4} = \frac{1}{16}\\ 1=16\cdot \frac{1}{16} = 2^4\cdot 2^{-4} = 2^{4-4} = 2^0.$$