Quotient Rule

When you divide two powers with the same base, you subtract the exponents: $x^a / x^b = x^{a-b}$.

For example, $2^5 / 2^2 = (2 \times 2 \times 2 \times 2 \times 2) / (2 \times 2) = 2^3$. The two factors of 2 in the denominator cancel two in the numerator, leaving $5 - 2 = 3$ factors.

This also explains why $x^0 = 1$: if you compute $x^3 / x^3 = x^{3-3} = x^0$, but anything divided by itself is 1.