Fiducia TogetherIndex laws in algebra
Powers with letters, and the fractional and negative cases.
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
The index laws apply to algebraic terms as to numbers: multiplying adds indices, dividing subtracts, a power of a power multiplies.
Where it applies
Both tiers; fractional and negative indices are higher.
How it works
A negative index is a reciprocal and a fractional one is a root, so x^(3/2) is the square root of x cubed.
The laws only apply within the same base, which is the rule most often broken.
How to use it in your work
Simplify the numbers and the letters separately, then combine.
Write fractional indices as roots when it makes the next step clearer.
Check the base is the same before applying any law.
Where to get help
Your teacher and your board's specification and mark scheme.
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.