Explanation

Index laws: aᵐ × aⁿ = aᵐ⁺ⁿ (same base, add powers). aᵐ ÷ aⁿ = aᵐ⁻ⁿ (same base, subtract powers). (aᵐ)ⁿ = aᵐⁿ (power of power, multiply).

Special cases: a⁰ = 1 (any number to power 0 equals 1). a⁻ⁿ = 1/aⁿ (negative power = reciprocal). a^(1/n) = ⁿ√a (fractional power = root).

Example: 2³ × 2⁴ = 2⁷ = 128. 8^(2/3) = (³√8)² = 2² = 4. Mastering these rules simplifies complex expressions significantly.