## 2012-08-29

### Fundamental Rule of Exponents

For a basic algebra class, given the rudimentary order-of-operations that looks like this:
1. Parentheses
2. Exponents & Radicals
3. Multiplication & Division
4. Addition & Subtraction
Then we have:

The Fundamental Rule of Exponents: Operations on same-base powers shift one place down in the order of operations.

Cases:
(1) Exponents will multiply powers, i.e., (am)n = am∙n. Example: (x6)2 = x12.
(2) Radicals will divide powers, i.e., n√am = am/n. Example: 3√x15 = x5.
(3) Multiplying will add powers, i.e., am∙an = am+n. Example: x4∙x7 = x11.
(4) Division will subtract powers, i.e., am/an = am−n. Example: x9/x2 = x7.

We've discussed this before, but I just recently decided to apply the name shown here to the pattern. It doesn't show up on a Google search yet, so I think it's fair-game to do so. Cheers!