What are indices in maths?

Answer 1

Indices, are powers to which a number is raised. They are written in superscript (to the top right of the thing you are raising to the power). Integer powers are the simplest and easiest to understand. ab is read "a to the power of b" and provided b is a whole number, it means you have to multiply a by itself b times.

21=2 since any number equals itself when raised to the power 1.

34=81 since 3*3*3*3=81

41/2=2. In this case the power of one half means we have to take the square root of 4.

The general case a1/b means we take the 'b'th root of a. So Square root, cube root etc.

Now we can also combine these:

ab/c means we first take the 'c'th root of a, and then raise it to the power of b.

So 272/3=9 since the cube root of 27 is 3, that is 33=3*3*3=27, and 32=9

If we have ab*ad, that can be simplified to ab+d, similarly ab/ad=ab-d.

Note 1/ab=a-b. Hence a0=ab/ab=1, which is important.

Answer 2

There are two types of indices. One type are the powers or exponents such as the 2 in x2 or the 0.5 in the square root of x and so on.

Then there are counters, for example in arrays. If you have a set of n observations for a variable x, then you can refer to all of them, together, as xi where 1 <= i <= n. In this case i is the index.