Explain how the rule that states that a^-n = 1/a^n is consistent with the rules that a^m/a^n = a^m-n and a^0 = 1 for a≠0.

Question

Explain how the rule that states that a^-n = 1 / aⁿ is consistent with the rules that a^m/aⁿ= a^m-n and a⁰ = 1 for a≠0.

Answer 1

If a ≠ 0, then a^-n = a^0-n = a⁰ / aⁿ = 1 / aⁿ. Here, in the second equality, the first of your stated rules was used, and in the last equality, the rule a⁰ = 1 for a ≠ 0 was used.