Negative and Fractional Indices — Interactive Lesson (Ages 14–16)

What is 8^−2/3? This 31-slide interactive lesson teaches negative and fractional indices, building up from the core index laws.

Mastering Negative and Fractional Indices at GCSE

Students recall the laws of indices for multiplying, dividing and raising a power to a power, then learn that a negative index means the reciprocal, so 2⁻³ = 1/8, and that a fractional index means a root, so 8^(1/3) = 2. They combine both rules, for example 27^(2/3) = 9 and 8^(−2/3) = 1/4, work with fractional bases such as (2/3)⁻² = 9/4 and finish with exam-style questions that combine several laws.

What’s Included

• 31-slide interactive lesson on negative and fractional indices
• Recap of the multiplication, division and power laws
• Rules for negative indices, fractional indices and both combined
• Fractional bases and worked examples
• Eleven quiz questions plus fill-in-the-blank and sorting activities

Key Benefits for Students

• Explains each rule with a short worked example
• Builds fluency evaluating without a calculator
• Prepares students for combined exam questions
• Instant feedback on answer questions

Why Teachers Love It

• No prep — ready for whole-class teaching on an interactive whiteboard
• A long, structured lesson that can be split across sessions
• Self-marking questions support independent practice
• Suits teaching, revision and homework
• Targets a topic that regularly appears on higher papers

Love this? You’ll love…

• Laws of Indices — Interactive Lesson (GCSE, Ages 14–16)
• Writing Numbers in Standard Form — Interactive Lesson (Ages 14–16)
• Estimating Powers and Roots — Interactive Lesson (Ages 14–16)

A dependable addition to a GCSE number and algebra topic, giving students a clear set of rules for a topic that often costs marks. Confident use of indices supports surds, standard form and algebraic manipulation.

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FAQ

What year group is this for? Years 10–11 (ages 14–16), GCSE.

Does it recap the basic index laws? Yes — before moving on to negative and fractional indices.

Is it self-marking? Yes, with instant feedback on the questions.