Introduction

So, what do you say to a pupil who asks why x ⁻¹ means 1 x https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315563688/17275003-2460-4424-8f87-3ffde62fbed0/content/eqn0_1a.tif"/> ? Sadly, I fear that too often the reply will be something like “It’s a definition: just make sure that you know it and get plenty of practice with negative and fractional indices because they’ll be in the exam.” Which leaves the enquirer wondering why x ⁻¹ should be defined in that way, as well as adding to the number of unconnected and seemingly arbitrary facts that have to be remembered and practised for the exam.