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Index Form - GCSE Maths Definition

Reviewed by: Dan Finlay

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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.

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Dan Finlay

Reviewer: Dan Finlay

Expertise: Maths Subject 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.

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