A LevelMaths: PureAQARevision Notes2. Algebra & Functions2.1 Laws of Indices & Surds2.1.1 Laws of Indices

Laws of Indices (AQA A Level Maths: Pure)

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Roger

Last updated

4 August 2023

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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:

Changing 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 Tip

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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Author: Roger

Expertise: Maths

Roger's teaching experience stretches all the way back to 1992, and in that time he has taught students at all levels between Year 7 and university undergraduate. Having conducted and published postgraduate research into the mathematical theory behind quantum computing, he is more than confident in dealing with mathematics at any level the exam boards might throw at you.