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Given $p \\in (1, \\infty)$, let $G$ be a Powers group, and let $\\alpha \\colon G \\to Aut(A)$ be an isometric action of $G$ on a unital $L^p$ operator algebra $A$ such that $A$ is $G$-simple. We prove that the reduced $L^p$ operator crossed product of $A$ by $G$, $F^p_{\\mathrm{r}}(G, A, \\alpha)$, is simple. Moreover, we show that traces on $F^p_{\\mathrm{r}}(G, A, \\alpha)$ are in correspondence with $G$-invariant traces on A. 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