Powers and Indices | Form 2 Mathematics

Powers and Indices

Powers and indices provide a compact notation for repeated multiplication and support efficient calculation.

Meaning and laws

In aⁿ, a is the base and n is the index. For the same non-zero base: aᵐ × aⁿ = aᵐ⁺ⁿ, aᵐ ÷ aⁿ = aᵐ⁻ⁿ, (aᵐ)ⁿ = aᵐⁿ, a⁰ = 1 and a⁻ⁿ = 1/aⁿ.

Worked examples

1. 2³ × 2⁴ = 2⁷ = 128.
2. 5⁶ ÷ 5² = 5⁴ = 625.
3. (3²)³ = 3⁶ = 729 and 2⁻³ = 1/8.

Practice

1. Simplify 7² × 7³ and 10⁵ ÷ 10².
2. Write 1/81 as a power of 3.
3. Evaluate (2³)² and explain why a⁰ = 1 for a ≠ 0.