Indices and Roots

This lesson covers the laws of indices (also called powers or exponents) and roots for AQA GCSE Mathematics. Understanding index laws is essential for simplifying expressions, working with standard form, and tackling algebraic problems. Some rules — particularly negative and fractional indices — are higher-tier content.

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What Are Indices?

An index (plural: indices) tells you how many times to multiply a number by itself.

• 2 cubed = 2 x 2 x 2 = 8
• 5 squared = 5 x 5 = 25
• 10 to the power of 4 = 10 x 10 x 10 x 10 = 10,000

Expression	Meaning	Value
3 squared	3 x 3	9
2 to the power of 5	2 x 2 x 2 x 2 x 2	32
10 cubed	10 x 10 x 10	1,000
7 to the power of 1	7	7
4 to the power of 0	(see below)	1

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The Laws of Indices

These laws apply when the base number is the same.