How to evaluate rational numbers to rational powers

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Is there a method besides a Taylor series to calculate $x^y$, where $x$ and $y$ are rational numbers? So for example, I require a method to calculate $2.128321\dots^{5.3212\dots}$ to a certain amount of digits. I realize that Taylor series are always an option, but is that what is used in calculators and computers? If not, what is used?