Question

How does the division rule for exponents help in understanding why anything to the zero power is 1?

Answer 1

In the division rule you subtract the exponents when dividing numbers with the same base. One rule for exponents is that exponents add when you have the same base. This works for any number x that you want to plug in except for x = 0,because 0/0 is indeterminate (it is like dividing zero by zero). No matter what number we use when it is raised to the zero power it will always be 1.