- Exponents & Radicals
- Multiplication & Division
- Addition & Subtraction
The Fundamental Rule of Exponents: Operations on same-base powers shift one place down in the order of operations.
(1) Exponentiation effectively multiplies powers, i.e., (am)n = am∙n. Example: (x6)2 = x12.
(2) Radicals effectively divide powers, i.e., n√am = am/n. Example: 3√x15 = x5.
(3) Multiplication effectively adds powers, i.e., am∙an = am+n. Example: x4∙x7 = x11.
(4) Division effectively subtracts 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!