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Laws of indices - EduqasUsing an index or power

Using indices, we can show a number times itself many times or as another way of writing a square or cube root. Indices make complex calculations that involve powers easier.

Part ofMathsNumber

Using an index or power

Explore updated revision resources for GCSE Maths: How to use an index or power, with step-by-step slideshows, quizzes, practice exam questions, and more!

An index, or a power, is the small floating number that goes next to a number or letter. The plural of index is indices.

Indices show how many times a number or letter has been multiplied by itself.

Here is a number written in index form:

Example of how to write numbers in index form. Base number shown as 2 and the power or index number shown as 4.

2 is the base number and 4 is the index or power.

24 is a short way of writing \(2 \times 2 \times 2 \times 2\).

\(a^2\) (read as '\(a\) squared’) means \(a \times a\). \(a\) has been multiplied by itself.

a^3 (read as ‘a cubed’) means a \times a \times a. a has been multiplied by itself three times.

Example of how to write letters in algebraic form. Base letter shown as A and the power or index number shown as 3.

\(a^4\) (read as ‘\(a\) to the power of 4’) means \(a \times a \times a \times a\). \(a\) has been multiplied by itself four times, and so on.