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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

Categories: maths Tags: , ,
1. 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. 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.