NumberDeep Dive

Higher Level: Fractional Indices

Part of Index LawsGCSE Mathematics

This deep dive covers Higher Level: Fractional Indices within Index Laws for GCSE Mathematics. Revise Index Laws in Number for GCSE Mathematics with 14 exam-style questions and 22 flashcards. This topic shows up very often in GCSE exams, so students should be able to explain it clearly, not just recognise the term. It is section 11 of 13 in this topic. Use this deep dive to connect the idea to the wider topic before moving on to questions and flashcards.

Topic position

Section 11 of 13

Practice

14 questions

Recall

22 flashcards

Higher Level: Fractional Indices

Fractional indices connect powers and roots:

  • a^(1/2) = √a (square root)
  • a^(1/3) = ∛a (cube root)
  • a^(m/n) = (ⁿ√a)ᵐ (root then power)

Example: 8^(2/3) = (∛8)² = 2² = 4

Or: 8^(2/3) = ∛(8²) = ∛64 = 4

Keep building this topic

Read this section alongside the surrounding pages in Index Laws. That gives you the full topic sequence instead of a single isolated revision point.

Practice Questions for Index Laws

Which of these is equivalent to a³ × a⁵?

  • A. a⁸
  • B. a¹⁵
  • C.
  • D. 2a⁸
1 markstandard

Simplify a⁵ × a³

1 markfoundation

Quick Recall Flashcards

Division Law
aᵐ ÷ aⁿ = aᵐ⁻ⁿ SUBTRACT the powers Example: 5⁶ ÷ 5² = 5⁴
Zero Power Law
a⁰ = 1 ANY number to power 0 equals 1 (except 0⁰ which is undefined) Examples: 5⁰ = 1, 100⁰ = 1

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