Fiducia TogetherIndices
Powers. The small raised number, and the rules for combining them.
Please note: This page explains a word or a process in education. It is general information about the system, the law and the guidance in England — not advice about your child, your school or your exam. If a decision is going against you, get advice from one of the free services we link to before you agree to anything or miss a deadline. If you are revising, check your own exam board's specification: boards word things differently and yours is the one that marks you.
What it is
An index is the power a number is raised to: in 5³, the index is 3. The plural of index is indices.
Where it applies
Both tiers, and it underpins standard form and algebra.
How it works
The laws: multiplying adds the indices, dividing subtracts them, a power of a power multiplies them. Anything to the power 0 is 1. A negative index means the reciprocal; a fractional index means a root, so x^½ is √x.
How to use it in your work
The laws only apply to the same base. x³ × y² does not simplify.
Negative and fractional indices are where marks are lost. x⁻² is 1/x², not −x².
Where to get help
Your teacher, your board's specification for what is on your paper, and Bitesize for worked examples. The maths song runs the topics in order.
Revise this with a song
These are ours. We write revision songs because a lot of people remember a tune when they cannot remember a page, and because revising out loud in the kitchen beats staring at a highlighter.
- The Maths Song The GCSE maths topics, in order.
Where to read more
Last reviewed 2026-08-28 by Fiducia Together · Next review due 2027-08-28
Please note: This page explains a word or a process in education. It is general information about the system, the law and the guidance in England — not advice about your child, your school or your exam. If a decision is going against you, get advice from one of the free services we link to before you agree to anything or miss a deadline. If you are revising, check your own exam board's specification: boards word things differently and yours is the one that marks you.