\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
Let \(E\) be a finite-dimensional \(\mathbb{K}\)-vector space with \(\dim E = n \ge 1\). Show that \(\dim(E^k) = k n\) for every integer \(k \ge 1\).
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