According to the product rule:
\[ x^0 * x^n = x^{0+n} = x^n \]
This implies \(x^0 = 1\). Another way to prove this involves the definition of exponents:
\[ x^{n+1} = x^n * x \]
In other words:
\[ x^n = \frac{x^{n+1}}{x} \]
If \(n=0\):
\[ x^0 = \frac{x^{1}}{x} = 1 \]