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Fractional Indices - GCSE Maths Definition

Reviewed by: Mark Curtis

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What are fractional indices?

Fractional indices are fractional powers of numbers, such as 8 to the power of 1 third end exponent. The fractional power 1 over n of a number represents the nth root of that number. For example, 8 to the power of 1 third end exponent represents cube root of 8 (the cube root of 8) which simplifies to 2.

The fractional power m over n can be thought of as either taking the nth root first then raising the answer to the power m, or raising to the power m first then taking the nth root of the answer (both give the same result, though one is often simpler than the other). For example, 8 to the power of 2 over 3 end exponent can be thought of as either open parentheses cube root of 8 close parentheses squared equals 2 squared or cube root of 8 squared end root equals cube root of 64, where both give the correct final answer of 4.

Fractional indices revision resources to ace your exams

Fractional indices are covered in our revision notes on Powers, Roots & Indices and Algebraic Roots & Indices from GCSE Maths. You can also have a go at our related exam questions and flashcards to test your understanding. Don’t forget to check out the GCSE maths past papers for more general exam revision.

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Mark Curtis

Reviewer: Mark Curtis

Expertise: Maths

Mark graduated twice from the University of Oxford: once in 2009 with a First in Mathematics, then again in 2013 with a PhD (DPhil) in Mathematics. He has had nine successful years as a secondary school teacher, specialising in A-Level Further Maths and running extension classes for Oxbridge Maths applicants. Alongside his teaching, he has written five internal textbooks, introduced new spiralling school curriculums and trained other Maths teachers through outreach programmes.

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