Exponents and Roots
Rules: | Rule | Formula | |------|---------| | Product | xᵃ × xᵇ = xᵃ⁺ᵇ | | Quotient | xᵃ / xᵇ = xᵃ⁻ᵇ | | Power | (xᵃ)ᵇ = xᵃᵇ | | Zero | x⁰ = 1 (x ≠ 0) | | Negative | x⁻ⁿ = 1/xⁿ | | Fraction | x^(1/n) = ⁿ√x |
Perfect squares: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225
Perfect cubes: 1, 8, 27, 64, 125, 216, 343, 512
Simplifying radicals: √72 = √(36 × 2) = 6√2. Factor out the largest perfect square.
Rationalizing the denominator: Eliminate radicals from denominators by multiplying numerator and denominator by the radical: 1/√3 × √3/√3 = √3/3.