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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

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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:List of index laws, A Level & AS Level Pure Maths Revision Notes

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 to the power of 4 equals left parenthesis 3 squared right parenthesis to the power of 4 equals 3 to the power of 2 cross times 4 end exponent equals 3 to the power of 8
    • Using the above can then help with problems like 9 to the power of 4 divided by 3 to the power of 7 equals 3 to the power of 8 divided by 3 to the power of 7 equals 3 to the power of 8 minus 7 end exponent equals 3 to the power of 1 equals space 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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    Roger

    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.