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Rules of Indices

Indices are numbers that are “to the power of” another number often written in the form ab. This is usually taken to mean a x a b times eg
23 = 2 x 2 x 2 = 8
–a is multiplies by itself b times

Note//In more advanced maths ab is often taken to mean exp(b ln(a))

There are a number of rules regarding how to manipulate indices of which the most important are listed below:

  1. ab x ac = ab+c
    since we have axa b times time axa c times giving axa b+c times
  2. ab ÷ ac = ab-c
    by similar logic to point 1
  3. (ab)c = abc
    since (ab)c = ab x ab… c times…ab
    but by (1) we get ab+b+…+b = abc
  4. a1/b = b√a
    Since by (3) (a1/b)b = ab/b = a
    but re arranging we get the result
    a1/b = b√a

If there any other rules that I haven’t included and aren’t immediately obvious from the above rules please leave them in the comments below

By David Woodford

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Categories: maths Tags: , ,
  1. Killian
    October 2, 2009 at 2:18 pm

    How would one solve the equation X to the power A multiplied by Y to the bower B

  2. October 2, 2009 at 6:25 pm

    you cant solve the equation unless it is equal to somthing. If you have
    X^A Y^B = Z
    then
    X = (ZY^{-B})^{\frac{1}{A}}

  3. Killian
    October 12, 2009 at 11:30 pm

    Btw, I forgot to say thanks for that. It really helped so I thought I’d come back and say thank you.

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