# 1 Powers

In mathematics, you often need to find a shorthand way of representing information or data. Nowhere is this need more obvious than when you wish to represent something like the product of 2 multiplied by itself 2, 6, 10, 15 or even 20 times.

Instead of writing 2 × 2 × 2 × 2 × 2 × 2, we write 2^{6}. This is read (and said) as ‘2 to the power 6’; 6 is the index or the power. In general, this means that

where *n* is called the index, or the power, of *a*. Both *a* and *n* can be either positive or negative numbers; *a** ^{−n}* represents .

So, and .

From this simple definition, you can now go on to look at power notation, or index notation as it is often called, in more detail.