Negative & Fractional Indices (GCSE Higher)

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About Course

Understand what zero, negative and fractional powers mean and evaluate expressions such as 2⁻³, 27^(2/3) and 8^(−2/3) without a calculator. Fractional indices are Higher tier GCSE content; this course builds them up from the index laws with checked worked examples.

Tutwoo is an independent learning provider. This course supports revision for GCSE Mathematics (Higher tier) in England. It is not produced or endorsed by any exam board and is not an accredited qualification.

© 2026 Tutwoo UK Limited. This course was created in-house by Tutwoo and is our original work. It is for your own learning only: please do not copy, share, record or resell it.

What Will You Learn?

  • Explain why any non-zero number to the power 0 equals 1
  • Evaluate negative powers as reciprocals, including of fractions
  • Evaluate fractional powers as roots, then powers
  • Combine the rules to simplify expressions and solve simple index equations

Course Content

Course Lessons

  • Index laws and the zero index
  • Negative indices
  • Fractional indices
  • Combining the rules

Sources & Further Reading
The official guidance this course is based on.

Final Assessment

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