## Indices

As you should know from GCSE, *x*^{3} is a shortening of . In the same way, any number to the power of n is that number multiplied by itself n times. To describe more detail, in the expression *x*^{3}, the *x* is referred to as the **base**, and the 3 as the **exponent**.

By always reducing the expression back to its basic parts it is possible to come to conclusions about how to treat numbers raised to powers in algebra.

### Multiplication

When you multiply indices you add the exponents together.

As you can see .

### Division

Division is, as expected, the opposite to multiplication. When you divide indices you subtract the exponents from each other.

Again this shows that

### Negative powers

Having done the above division, we begin to ask ourselves what happens when we have a fraction that has a higher exponent on the bottom than the top.

Using the trusted method of showing each x seperately we obtain:

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