Powers and Roots – GCSE Maths Revision and Worksheets

What you need to know:

Indices (or powers) are a shorthand way of expressing multiplication by the same number multiple times. You should become very familiar with the idea that 6^3 is a more compact way of expressing the multiplication of 3 sixes together, or in other words 6^3 = 6 \times 6 \times 6. Similarly, with algebra a^4 = a \times a \times a \times a.

You are required to understand the meaning of powers, and apply it where necessary, but you are furthermore expected also to memorise all the squares up 15, i.e. 1^2 = 1, 2^2 = 4, 3^2 = 9, … up to and including 15^2 = 225.

It also necessary to understand and work with roots, which act as the inverse to powers/indices (much in the same sense that multiplication acts as the inverse to division). That is to say, if you take 4 to the 3^rd power (i.e. you do 4^3 and get 64), and then you take the 3^rd root of the answer, denoted by \sqrt[3]{64}, then you end up back where you started, with 4. Roots exist to perform the exact opposite role in mathematics to taking the power of something.