NumberDeep Dive

Higher Level: Fractional and Negative Indices

Part of Powers & Roots · GCSE GCSE Mathematics revision

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.

Topic position

Section 11 of 14

Practice

15 questions

Recall

22 flashcards

Higher Level: Fractional and Negative Indices

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!

Keep building this topic

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

Worked Example 4: Estimating Roots Common Mistakes to Avoid The Power of Powers Understanding Powers and Roots

Practice Questions for Powers & Roots

What is the value of 2⁻³?

A. -8
B. -6
C. ⅛
D. ⅓

1 markfoundation

Explain why x⁻¹ = 1/x

2 markshigher

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

15 questions on Powers & Roots — practise free

Instant marking, adaptive difficulty, and 22 spaced repetition flashcards. Free until your GCSEs.

Try PrepWise Free

Worked Example 4: Estimating Roots

Common Mistakes to Avoid