Irrationality of powers of $\pi$

Everyone recognizes that $\pi$ is an illogical number, and also one can describe this page for the evidence that $\pi^{2}$ is additionally illogical.

What concerning the highers powers of $\pi$, definition is $\pi^{n}$ illogical for all $n \in \mathbb{N}$ or does there exists a $m \in \mathbb{N}$ when $\pi^{m}$ is sensible.

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2019-05-09 11:30:50
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What Robin meant :

If $\pi^{n}$ was sensible, after that $\pi$ would certainly not be transcendental, as though the origin of $ax^{n}-b = 0$ for some integers $a,b$.

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2019-05-10 07:33:00
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