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An irrational number cannot be represented by $\frac{p}{q}$ where $p$ and $q$ are integers.

And when we encounter exponents with decimal points, it is a possible way and a rather simple one to turn the exponent into the previous mentioned $\frac{p}{q}$ form and then figure the whole thing out using $a^{\frac{p}{q}}=\sqrt[q]{a^p}$.

So this way doesn't work for irrational exponents. How does a calculator do the job? Is it simply multiplication like $a^\pi=a^3\times a^{0.1}\times a^{0.04} \cdots$? Or with a more practical method?

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1 Answer

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There is an identity

$$x^y = \exp(y \log(x))$$

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