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Proof

(related to Proposition: Nth Powers)

By hypothesis, $n\in\mathbb Z$ is an integer. Note that, together the with the multiplication operation of real numbers "$\cdot$", the set $(\mathbb R,\cdot )$ is an Abelian group. Therefore, the $n$-th power function $f:x\to x^n$ is well-defined as an exponentiation of $x\in\mathbb R$.

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References

Bibliography

1. Forster Otto: "Analysis 1, Differential- und Integralrechnung einer Veränderlichen", Vieweg Studium, 1983