When calculating a number to a fractional exponent or fractional nth root, in what cases is there both a positive and negative solution as opposed to just a positive or just a negative solution?
2026-03-29 15:16:52.1774797412
Sign of Fractional Exponents
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Expanding the comment of user164587:
A $n$-th root of $a$ is by definition a solution of $$x^n=a.$$ If the exponent is odd, the function $$x\longmapsto x^n$$ is increasing and the equation has only one solution (the function $y=x^n$ and the horizontal line $y=a$ intersect at a single point).
But if $n$ is even...