Exercise 1, § 3

General Topology, IV, 387

Let $x$ be a real number $\geqslant 0$ and let $p$ and $q$ be two integers $> 0$ . Prove the relations

(x^{1/p})^{1/q} = x^{1/pq}, \quad (x^p)^{1/q} = (x^{1/q})^p, \quad x^{1/p} x^{1/q} = (x^{p+q})^{1/pq}.

Solution

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