Grade 10 · Theory
Exponents
Algebraic expressions · about 3 min
Visual overview: Exponents1 MIN READ
2 study sections · pause after each one and recall the key ideaExponent laws let you simplify powerful-looking expressions quickly, and they underpin scientific notation and growth formulae.
Key points- aᵐ × aⁿ = aᵐ⁺ⁿ and aᵐ ÷ aⁿ = aᵐ⁻ⁿ (same base only).
- (aᵐ)ⁿ = aᵐⁿ, and (ab)ᵐ = aᵐbᵐ.
- a⁰ = 1 (a ≠ 0) and a⁻ᵐ = 1/aᵐ.
- Fractional exponents are roots: a^(1/n) = ⁿ√a.
- Base — the number being raised to a power.
- Exponent — how many times the base is multiplied by itself.
EXAM TIP
convert everything to prime bases (8 = 2³, 27 = 3³) before applying the laws — most exam questions unlock immediately.