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Laws of Indices (Edexcel AS Maths: Pure): Revision Note

Exam code: 8MA0

Written by: Roger B

Reviewed by: Dan Finlay

Updated on 2 July 2026

Laws of indices

What do I need to know about laws of indices?

Laws of indices (or index laws – 'index' is the singular, 'indices' is the plural) allow you to simplify and manipulate expressions involving powers
The index laws you need to know and use are summarised here:

How do I change the base of a term?

Sometimes expressions involve different base values
You can use index laws to change the base of a term to simplify an expression involving terms with different bases
- For example $9^{4} = {(3^{2})}^{4} = 3^{2 \times 4} = 3^{8}$
- Using the above can then help with problems like $9^{4} \div 3^{7} = 3^{8} \div 3^{7} = 3^{8 - 7} = 3^{1} = 3$

Examiner Tips and Tricks

Index laws only work with terms that have the same base, so something like 2³ × 5² cannot be simplified using index laws

Worked Example

Index laws example, A Level & AS Level Pure Maths Revision Notes

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