For a sequence of elements $\underline{a}= a_{1}, ..., a_{r} \in R$, let $K^{\bullet}(\underline{a};R)$ be the Koszul complex generated by $\underline{a}$. Let $\underline{a}^{v} = a_{1}^{v_{1}}, ..., a_{r}^{v_{r}} \in R$.
My question: if $K^{\bullet}(\underline{a};R)$ is acylic is $K^{\bullet}(\underline{a}^{v};R)$ acylic?
My thoughts: if $\underline{a}$ is regular and R is nice enough this is true. When R is nice, regular sequences always give acyclic Koszul complexes and powers of regular sequences are regular. So this means and meaningful counterexamples would have to avoid the case of $R$ Noetherian, local and $R$ Noetherian,graded with $\underline{a}$ homogeneous of positive degree.