Wednesday, August 29, 2012

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!


3 comments:

  1. I've seen this presented as the "Exponential Law" or the "Law of Exponents".

    For some stupid reason, there is no standard name for this process.

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    Replies
    1. Interesting, but I don't see either of those with any hits on Google. What I do see a lot of (and common in books) is "Laws of Exponents" in the plural, listing a half-dozen disconnected relationships. It's weird, but I've never seen any place abstract it out to one single concept before.

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  2. Just discovered the only other place I've seen online where this same observation is described (without any given name), at the site OakRoadSystems. Nice presentation.

    ReplyDelete