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Negative Indices - GCSE Maths Definition

Reviewed by: Mark Curtis

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What are negative indices?

Negative indices are negative powers of numbers, such as 5 to the power of negative 2 end exponent. A negative power is the same as 1 over the positive power, so 5 to the power of negative 2 end exponent equals 1 over 5 squared which can be simplified to 1 over 25 (or 0.04 as a decimal). A common mistake is to write 5 to the power of negative 2 end exponent as negative 25, but negative powers of positive numbers do not actually give negative answers (they give answers that are positive fractions instead).

Negative powers are used when measuring small lengths, for example 10 to the power of negative 3 end exponent representing 0.001 from 1 over 10 cubed equals 1 over 1000, and are also used a lot in algebra, such as x to the power of negative 3 end exponent representing 1 over x cubed.

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Mark Curtis

Reviewer: Mark Curtis

Expertise: Maths Content Creator

Mark graduated twice from the University of Oxford: once in 2009 with a First in Mathematics, then again in 2013 with a PhD (DPhil) in Mathematics. He has had nine successful years as a secondary school teacher, specialising in A-Level Further Maths and running extension classes for Oxbridge Maths applicants. Alongside his teaching, he has written five internal textbooks, introduced new spiralling school curriculums and trained other Maths teachers through outreach programmes.

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