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
2³ = 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:

1. a^b x a^c = a^b+c
   since we have axa b times time axa c times giving axa b+c times
2. a^b ÷ a^c = a^b-c
   by similar logic to point 1
3. (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
4. 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