Exponent laws let you simplify powerful-looking expressions quickly, and they underpin scientific notation and growth formulae.

• 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.