How to use the Rules of Indices

How to use the rules of indices is very useful in maths ..

..as it is a convenient way of writing down large numbers that have many repeating terms. It’s quicker to write 10^6 than 1,000,000 each time. The index (sometimes called the exponent) simply says how many times the number is used in the calculation.

So 10³ is the same as 10 x 10 x 10 which equals 1000. This is usually read as 1 thousand, but could be read as ’10 cubed,’ ’10 to the third power,’ or ‘ 10 to the power of 3.’

… or 10^6 is the same as 10 x 10 x 10 x 10 x 10 x 10 which equals 1,000,000. As before this is read as 1 million, but could be ’10 to the power of 6′ or ’10 to the 6th power.’

I know it’s confusing but you’ll get used to it..

Actually, this is only part of the story. The rules of indices are quite useful when we are multiplying or dividing really large numbers (or very, very small ones). We tend to write these as ‘scientific notation’ as it is much easier than worrying about a lot of zero’s – which are very easy to miscount.

For instance the distance from Earth to the nearest star outside the solar system is approximately 25,700,000,000,000 miles. If we went there and back it would be 51,400,000,000,000 miles – much easier to write 5.14 x 10^13 – and it doesn’t feel as far.

Multiplication and division of indices (or powers) with examples. GCSE grade 4 around 2 marks.

or, watch on YouTube:

How to use the Rules of Indices 1

How to use the Rules of Indices 2

 

Here’s some other posts that might be of interest:

How to work with indices – GCSE maths practice questions

How to work out compound interest using a formula – GCSE mathematics