xᵃ × xᵇ = x^(a+b) — multiplying powers: add exponents
xᵃ ÷ xᵇ = x^(a−b) — dividing powers: subtract exponents
(xᵃ)ᵇ = x^(ab) — power of a power: multiply exponents
x⁰ = 1 — anything to the power of zero is 1
x⁻ⁿ = 1/xⁿ — negative exponent = reciprocal
x^(1/n) = ⁿ√x — fractional exponent = root
What is a negative exponent?
A negative exponent means the reciprocal. 2⁻³ = 1/2³ = 1/8 = 0.125.
What is a fractional exponent?
A fractional exponent represents a root. x^(1/2) = √x. x^(1/3) = ∛x. x^(2/3) = (∛x)².