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Index Form: GCSE Maths Definition

Dan Finlay

Written by: Dan Finlay

Reviewed by: Lucy Kirkham

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Contents

  1. 1. What is index form?
  2. 2. Index form revision resources to ace your exams

What is index form?

In GCSE maths, a number is written in index form if it is of the form space a to the power of b. The value space a is called the base and the value space b is called the index. For example, 25 can be written in index form as 5 squared. The number 64 can be written as 8 squared or 4 cubed or even 2 to the power of 6.

Index form can also be used to write numbers in standard form, which is where a number is written as a cross times 10 to the power of k where 1 less or equal than a less than 10 and k is an integer. Index form can be used to represent the prime factor decomposition of a number by using prime numbers for the bases. The prime factor decomposition of 20 is 2 cross times 2 cross times 5, but questions will commonly ask you to give your answer using index form which would be 2 squared cross times 5.

The laws of indices can be used when numbers are written in index form. A root of a number can be written in index form using a fraction, space n-th root of a equals a to the power of 1 over n end exponent. Also a reciprocal can rewritten in index form using a negative number, space 1 over a equals a to the power of negative 1 end exponent. If two numbers are written in index form with the same base number then they can be multiplied or divided quickly using the laws of indices space x to the power of a cross times x to the power of b equals x to the power of a plus b end exponent and x to the power of a over x to the power of b equals x to the power of a minus b end exponent.

Index form revision resources to ace your exams

Learn more about index form with our revision notes. To test your knowledge, try our exam questions related to index form.

For quick-fire GCSE maths revision use our collection of interactive flashcards for GCSE maths. We also have past papers for your exam practice.

Explore our GCSE maths revision resources

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Author
Reviewer
Dan Finlay

Author: Dan Finlay

Expertise: Maths Lead

Dan graduated from the University of Oxford with a First class degree in mathematics. As well as teaching maths for over 8 years, Dan has marked a range of exams for Edexcel, tutored students and taught A Level Accounting. Dan has a keen interest in statistics and probability and their real-life applications.

Lucy Kirkham

Author: Lucy Kirkham

Expertise: Head of STEM

Lucy has been a passionate Maths teacher for over 12 years, teaching maths across the UK and abroad helping to engage, interest and develop confidence in the subject at all levels.Working as a Head of Department and then Director of Maths, Lucy has advised schools and academy trusts in both Scotland and the East Midlands, where her role was to support and coach teachers to improve Maths teaching for all.

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