Powers, Roots and Index Laws

This lesson covers squares, cubes, square roots, cube roots, and the index laws (including negative, zero and fractional indices for Higher tier). These topics are essential for the Edexcel GCSE Mathematics (1MA1) specification and are frequently tested across all three papers.

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Key Vocabulary

Term	Meaning
Power / Index / Exponent	The small number written above and to the right, e.g. the 3 in 2³
Base	The number being raised to a power, e.g. the 2 in 2³
Square number	A number multiplied by itself, e.g. 5² = 25
Cube number	A number multiplied by itself three times, e.g. 4³ = 64
Square root (√)	The inverse of squaring: √25 = 5
Cube root (∛)	The inverse of cubing: ∛64 = 4

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Square Numbers and Square Roots

Square Numbers to Know