Exponents from scratch
An exponent is a shorthand for repeated multiplication: 2^5 = 2·2·2·2·2 = 32. A negative exponent flips it to a reciprocal: 2^(−3) = 1/2^3 = 1/8.
Fractional exponents are roots: x^(1/2) = √x, x^(1/3) = ∛x. This is what unifies exponents and roots into a single concept.
Useful identities: a^m × a^n = a^(m+n), (a^m)^n = a^(m·n), and a^0 = 1 for any non-zero a.