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 14 in this topic. Use this deep dive to connect the idea to the wider topic before moving on to questions and 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
Practice questions for Index Laws
Which of these is equivalent to a³ × a⁵?
Simplify a⁵ × a³
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