Rational exponentiation?

Asked Nov 06 '13 at 15:22

Active Nov 06 '13 at 15:22

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Consider the following operation:

$\left(\frac{a}{b}\right)^\frac{n}{m}$

where $a, n\in\mathbb{Z}$ and $b, m\in\mathbb{N^*}$.

My question is: when the result is a rational number, how (formula or algorithm) do you compute $c\in\mathbb{Z}, d\in\mathbb{N^*}$ in:

$\frac{c}{d}=\left(\frac{a}{b}\right)^\frac{n}{m}$

asked Nov 06 '13 at 15:22

Vincent

1

Related: http://math.stackexchange.com/questions/126419/determine-if-p-qa-b-is-rational?rq=1 – Rustyn Nov 06 '13 at 15:42
Here is a hint: If $x = 1.23456789$ is a rational number, then $x = \dfrac{123456789}{100,000,000}$. – Björn Friedrich Aug 23 '15 at 08:06

0 Answers0