Rules of Fractional Exponents
Translating powers into roots:
RULE 1
Denominator is Root
The bottom denominator b indicates the b-th root: x^(1/b) = ᵇ√x.
RULE 2
Numerator is Power
The top numerator a is the exponent applied to the base or root: (ᵇ√x)ᵃ.
RULE 3
Negative Exponents
Negative rational exponents flip the base into reciprocal: x^(-a/b) = 1 / x^(a/b).
RULE 4
Even Root Property
Even roots of negative bases yield imaginary complex numbers.