How this calculator works
Reduce the exponent before interpreting it as a root and a power. A positive base accepts every rational exponent with a non-zero denominator. A negative base has a real result when the reduced denominator is odd; the reduced numerator determines the sign. Zero needs a positive exponent. Reverse base mode returns the positive branch. Numerator and denominator recovery require integer components.
Formula
x^(n/d) = (root_d(x))^n after reducing n/d; for x < 0 the reduced d must be odd.
Worked example
(-8)^(2/3) = (-2)^2 = 4. Also, 16^(-1/2) = 1/sqrt(16) = 1/4.
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Frequently asked questions
Why reduce the exponent first?
Equivalent rational exponents must have the same result. For example, (-8)^(2/6) uses the reduced exponent 1/3 and equals -2.
Can I use a negative denominator?
Yes. Its sign moves to the numerator before the exponent is interpreted.
What does a negative exponent mean?
It takes the reciprocal of the corresponding positive power. A zero base is therefore invalid for a negative exponent.