zero exponent

Any nonzero number raised to the power zero equals 1: b^0 = 1. This looks strange at first — multiplying something “zero times” seems like it should give nothing — but it is the only choice that keeps the exponent rules consistent.

Here is the reasoning. By the quotient rule, b^n / b^n = b^(n−n) = b^0. But any nonzero quantity divided by itself is 1. So b^0 must equal 1. Another way to see it: going down the powers of 2 — 8, 4, 2 — each step divides by 2, and the next step gives 2^0 = 1.

The catch is the base. The expression 0^0 is left undefined (or context-dependent) because two reasonable patterns disagree, so the clean rule b^0 = 1 is stated only for nonzero b. For every other base, large or small, the zero power is exactly 1.