If you think about it, exponents is simply repeated multiplication. Knowing that, we can apply what we already know about multiplying negative numbers. Exponents with negative and zero bases are treated differently, as well as power of zero exponents. Order of operations will help us make sense of those circumstances.
The progression of powers from zero to any non-zero number follows a pattern and can be logically explained. After watching this, it will make sense why any non-zero number to the zero power equals one.