NumberStudy Notes

Worked Example 4: Negative Indices

Part of Index Laws — GCSE Mathematics

This study notes covers Worked Example 4: Negative 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 10 of 13 in this topic. Use this study notes to connect the idea to the wider topic before moving on to questions and flashcards.

Topic position

Section 10 of 13

Practice

14 questions

Recall

22 flashcards

Worked Example 4: Negative Indices

Evaluate: 3⁻²

Solution

Using a⁻ⁿ = 1/aⁿ

3⁻² = 1/3²

= 1/9

Answer: 1/9

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.

Worked Example 3: Power of a Power Higher Level: Fractional Indices The Rules of Powers What Are Index Laws?

Practice Questions for Index Laws

Which of these is equivalent to a³ × a⁵?

A. a⁸
B. a¹⁵
C. a²
D. 2a⁸

1 markstandard

Simplify a⁵ × a³

1 markfoundation

Quick Recall Flashcards

Zero Power Law

a⁰ = 1 ANY number to power 0 equals 1 (except 0⁰ which is undefined) Examples: 5⁰ = 1, 100⁰ = 1

Division Law

aᵐ ÷ aⁿ = aᵐ⁻ⁿ SUBTRACT the powers Example: 5⁶ ÷ 5² = 5⁴

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Worked Example 3: Power of a Power

Higher Level: Fractional Indices