Indices: GCSE Maths revision
Indices are powers. The laws let you multiply, divide and raise powers to powers without expanding huge numbers.
Index laws
- aᵐ × aⁿ = aᵐ⁺ⁿ
- aᵐ ÷ aⁿ = aᵐ⁻ⁿ
- (aᵐ)ⁿ = aᵐⁿ
- a⁰ = 1 (a ≠ 0)
- a⁻ⁿ = 1 / aⁿ
Try these questions
Cover the answers and have a go first. Worked solutions are underneath.
Simplify x³ × x⁵
Simplify y⁷ ÷ y²
Simplify (a²)⁴
Evaluate 5⁰
Write 3⁻² as a fraction
Common mistakes
- Multiplying the indices instead of adding when multiplying powers.
- Writing a⁻² as −a² instead of 1/a².
Answers and working
Frequently asked questions
What about fractional indices?
Higher tier: a^(1/2) is √a and a^(1/3) is the cube root. a^(m/n) is the nth root of aⁿ.
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