## Rules of Indices

Indices are numbers that are “to the power of” another number often written in the form a^{b}. This is usually taken to mean a x a b times eg

2^{3} = 2 x 2 x 2 = 8

–a is multiplies by itself b times

**Note//**In more advanced maths a^{b} 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:

- a
^{b}x a^{c}= a^{b+c}

since we have axa b times time axa c times giving axa b+c times - a
^{b}÷ a^{c}= a^{b-c}

by similar logic to point 1 - (a
^{b})^{c}= a^{bc}

since (a^{b})^{c}= a^{b}x a^{b}… c times…a^{b}

but by (1) we get a^{b+b+…+b}= a^{bc} - a
^{1/b}=^{b}√a

Since by (3) (a^{1/b})^{b}= a^{b/b}= a

but re arranging we get the result

a^{1/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

Advertisements

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

you cant solve the equation unless it is equal to somthing. If you have

then

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