DfE statement N7 · Number
Calculating with roots and indices
Calculating with roots and indices is content statement N7 of the DfE GCSE mathematics subject content, in the number area. It is on both tiers, with a Higher-only part, and it is examined without a calculator. Below is what the specification actually requires, the 4 mistakes that cost marks on this topic most often, and practice questions written to the statement — original questions, not past papers.
What the specification says
The DfE subject content for GCSE mathematics states, verbatim: "Calculate with roots, and with integer and fractional indices." (statement N7). Every awarding organisation — Pearson Edexcel, AQA and OCR — must cover it, so the wording is the same whichever specification your school follows.
Tier
Both tiers, but part of it is Higher only. Foundation covers the statement except for the following, which the DfE prints in bold and reserves for Higher: "and fractional". Everything else in the statement is Foundation content.
Calculator
This is non-calculator territory. Questions on it belong naturally on Paper 1, where written method is all you have — so practise it that way rather than with a calculator to hand.
Common mistakes
- Adding indices when the bases differ: 2³ × 3³ is not 6⁶ or 6³ by the index laws you were taught for a common base.
- Treating a negative index as a negative number: 2⁻³ is 1/8, not −8.
- Reading x^(1/2) as half of x. A fractional index is a root — x^(1/2) is √x and x^(2/3) is the cube root of x squared.
- Adding rather than multiplying for a power of a power: (x³)² answered as x⁵ instead of x⁶.
Sample questions (10 of 30)
Nearby statements
Questions people ask
Is calculating with roots and indices on Foundation or Higher?
Both, but not all of it. The parts the DfE prints in bold — "and fractional" — are Higher only; the rest is Foundation content.
Can I use a calculator for calculating with roots and indices?
Not on Paper 1, which is where this normally appears. Paper 1 is non-calculator for both tiers and carries the same 80 marks as each of the other two papers.
What is the single most common mistake here?
Adding indices when the bases differ: 2³ × 3³ is not 6⁶ or 6³ by the index laws you were taught for a common base.
Are these past paper questions?
No. Every question is original, written to this DfE content statement and checked before publication. We do not host past papers or mark schemes.
Back to Number at Foundation or at Higher.