Exponentiation
For every number a ≠ 0 you can calculate that a0 = 1.
Explanation
During exponentiation, you multiply the base so often with itself as indicated by the exponent. You do this only once, and so you can write
Usually you omit the number 1, but it's there anyhow. The product is not affected by the factor 1, because
a3 = 1 · a · a · a
a2 = 1 · a · a
a1 = 1 · a
a0 = 1
Zero as exponent indicates that the number 1 is not multiplied with the base, so only 1 remains. Moreover, this syntax provides 00 ≝ 1 and that is beautiful.