Seems rational

Algebra Level 3

If there are four distinct numbers \(p\), \(q\), \(r\), and \(s\) such that \(\dfrac{p}{q} = \dfrac{r}{s} \) holds true, then is

\[\large x^{\frac{p}{q}} = x^{\frac{r}{s}} \]

also true for all \( x \in \mathbb{C}\)?

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