Preview of advanced index laws:
- Fractional: x^(1/2) = √x, x^(1/3) = ∛x
- Negative: x^(-1) = 1/x, x^(-2) = 1/x²
- Combined: 8^(2/3) = (∛8)² = 2² = 4
These connect powers and roots as inverse operations!
This deep dive covers Higher Level: Fractional and Negative Indices within Powers & Roots for GCSE Mathematics. Revise Powers & Roots in Number for GCSE Mathematics with 15 exam-style questions and 22 flashcards. This is a high-frequency topic, so it is worth revising until the explanation feels precise and repeatable. 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.
Practice questions for Powers & Roots
What is the value of 2⁻³?
Explain why x⁻¹ = 1/x
Quick recall flashcards
Powers of 10
10¹ = 10
10² = 100
10³ = 1,000
10⁴ = 10,000
10⁵ = 100,000
10⁶ = 1,000,000
Pattern: n zeros after 1
Cubes: 1³ to 5³
1³ = 1
2³ = 8
3³ = 27
4³ = 64
5³ = 125