To divide two powers with the same base we have to transform them into a single power, which we will check in this window.

Go on practising powers in the window above, but now write the same index in the two powers. Thus, you will get a power of index 0. Notice the value of that power.

You will have discovered that:

A power of index 0 equals 1.

In order to see the changes step by step, click on the blue triangle in the top of the window.
Do not continue until you understand each step completely. You can also change the values of the base and the index with the buttons below.

Go on practising powers in the window above, but now the index of the divisor must be larger than the index of the dividend. Thus, you will get a power of a negative index. Notice the value of that power.

You will have discovered that:
A power of a negative index equals the reciprocal of that power with a positive index.