Rules of Indices – GCSE Maths Revision and Worksheets

What you need to know:

There are three laws of indices, applicable to both algebra and numbers, that you must know and be able to use. Note that the first two rules require that both the terms involved in the expression have the same base. The laws are as follows, for any value of a, m, or n.

• FIRST LAW: Multiplying terms means that we add the powers. See:

a^m \times a^n = a^{m+n}

• SECOND LAW: Dividing terms means that we subtract the powers. See:

a^m \div a^n = \frac{a^m}{a^n} = a^{m-n}

• THIRD LAW: If we take a power of a power, then the powers are multiplied. See:

\left(a^m\right)^n = a^{mn}

It is also useful to know that for any value of a, a^0 = 1, and a^1 = a.