Rational Exponent

Solution 1:

$1/3$ and $2/6$ are the same number, so if we need to evaluate $(-8)^{1/3}$ and $(-8)^{2/6}$, we must make sure that the result is the same in each case. So yes, you need to reduce a fractional exponent to its lowest terms before applying it to a negative operand.

Having said that, the exponential function $x^y$ doesn't seem to be useful for negative $x$ and rational $y$, except perhaps when $y$ is of a special form to begin with, like $1/n$ for instance. So the question doesn't usually arise. Where did this question come from?

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