I explain the reason we define negative and zero exponents as we do. We're just extending the pattern we have created for positive numbers into other types of numbers by repeatedly dividing by the base.
This is an example of how mathematicians EXTEND definitions. We only defined exponentiation with positive bases, but, using the original definition and noticing some patterns, we created a more general definition in which all our previous laws apply.
I forgot to mention-- negative exponents are undefined when the base is 0. This is because we can't divide by 0!
