## Exponents

An index, power or exponent is a way of shortening expressions such as 4 × 4 × 4 to 43

In algebra p5 is a short way of writing p × p × p × p × p.
(p × p × p × p × p is the expanded form.)

In pthe p is called the variable, pronumeral or base and the 5 is called the index, power or exponent.

The plural of index is indices.
Sometimes in algebra the multiplication sign is replaced by a full stop.

e.g. 4p × 3q can be written 4p.3q

### Difference between 2p and p2

A common mistake is to think that p multiplied by p is equal to 2p!
Remember:

 p + p 2p p × p p2

### Writing Terms in Index Form

When variables and numbers are multiplied together there are three steps:

1. The numbers are multiplied together first and put at the front (called the coefficient).
2. The variables are grouped together using exponents.
3. The variables and their exponents are written in alphabetical order.

Examples:

 Expanded form Index form 5 × m × m 5m2 5 × m × 5 × m × m × m 25m4 4 × m × 5 × n × m × n × m 20m3n2 -2 × m × m × 3 × m -6m3

### Special Exponents

There are two rules for "special" exponents.

1. Any number or variable to the power of zero = 1
2. Any number or variable to the power of one = itself

Examples

 90 1 x0 1 5p0 5 × 1 = 5 31 3 10x1 10.x = 10x