Rules of Indices

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Rules of Indices

Number: Interactive Lessons
GCSE Mathematics lesson on fractional powers and indices featuring Evaluate, Simplify, and Prove tasks. Examples include simplifying (x^6w^10/25)^(3/2) using fractional index laws and evaluating 2^3 × 8^(2/3) √8. This differentiated approach builds fluency with rational exponents, surds, and index notation. Perfect for Edexcel, AQA, OCR GCSE maths students mastering fractional indices, powers of fractions, and algebraic simplification.
Ages 14 - 16

Indices with Fractional Powers

Complete GCSE maths lesson and worksheet on fractional indices.
Number: Interactive Lessons
GCSE Mathematics lesson on negative powers and indices featuring three skill levels: Evaluate (writing 1/32 as a power of 2), Simplify, and Prove (showing that (2x^-3)^-2 equals x^6/4). This differentiated approach helps students master negative index laws through progressive problem-solving. Suitable for Edexcel, AQA, OCR GCSE maths students learning laws of indices, exponent rules, and algebraic manipulation with negative powers.
Ages 14 - 16

Indices with Negative Powers

Complete GCSE maths lesson and worksheet on negative powers.
Number: Interactive Lessons
Rules of Indices
Ages 14 - 16

Rules of Indices

Students learn how to simplify expressions using the rules of indices.
Number: Interactive Lessons
Indices with Negative Powers
Ages 11 - 13

Indices with Negative Powers

Students learn how to write indices with negative powers as fractions.
Number: Interactive Lessons
Applying the Rules of Indices
Ages 16 +

Index Laws

Students learn how to simplify expressions with fractional and negative powers.
Number: Free Resources
A horizontal transition presentation slide from Mr Mathematics titled Factorising with Powers with a top-right corner ribbon reading Pure 1 AS Maths. The algebraic problem shows an identity where open parenthesis 1 plus y close parenthesis to the power of a half plus 3 times open parenthesis 1 plus y close parenthesis to the power of 3 over 2 is identical to the square root of 1 plus y times open parenthesis a plus b y close parenthesis. A blue box prompt reads Find a and b.
Ages 16 +

Expanding and Factorising Expressions with Fractional Powers

Students learn how to expand and factorise an algebraic expression with fractional powers.
Number: Interactive Lessons
Change of Base
Ages 16 +

Change of Base

How to use the power rule of indices to change a base.
Number: Interactive Lessons
Solving Equations with Indices
Ages 14 - 16

Solving Equations with Change of Base

How to solve equations with indices using the power rule.
Number: Interactive Lessons
Power Rule of Indices
Ages 11 - 13

Power Rule of Indices

Key Stage 3: Number: Rules of Indices
Number: Interactive Lessons
Higher GCSE revision lesson on problem solving with indices featuring an exam-style equation involving powers, simplifying expressions and solving indices equations.
Ages 14 - 16

Problem Solving with Indices

GCSE / IGCSE revision lesson on advanced index notation.

Mr Mathematics Blog

Developing Mathematical Thinking Beyond Procedural Fluency

July 10, 2026
A research-backed case exploring why over-reliance on automated math homework platforms and repetitive worksheets lowers student expectations, and how departments can build genuine mathematical thinking.

Converting Between Fractions, Decimals and Percentages

July 4, 2026
How to teach converting between fractions, decimals and percentages.

From Key Skills to Deep Connections: Problem Solving in Secondary Maths

June 28, 2026
Four problem solving lessons to develop student's mathematical reasoning and communication skills.