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Powers of (monomial) ideals is a subject that still calls attraction invarious ways. In this paper we present a nice presentation of high powers ofideals in a certain class in $\mathbb K[x_1, \ldots, x_n]$ and $\mathbb K[[x_1,\ldots, x_n]]$. As an interesting application it leads to an algorithm forcomputation of the Ratliff--Rush operation on ideals in that class. TheRatliff--Rush operation itself has several applications, for instance, if $I$is a regular $\mathfrak m$-primary ideal in a local ring $(R,m)$, then theRatliff--Rush associated ideal $\tilde I$ is the unique largest idealcontaining $I$ and having the same Hilbert polynomial as $I$.

Powers of monomial ideals and the Ratliff-Rush operation