Given i.i.d. Bernoulli( $\theta$ ) r.v.s $X_{1}, X_{2}, \ldots, X_{m},$ I'm interested in finding UMVUE of $(1-\theta)^{1/k}$, where $k$ is a positive intger. .

I know that $\sum X_{i}$ is my sufficient statistic from using the Factorization Theorem, but I'm having trouble proceeding from there.

I understand that if I can find an unbiased function of the sufficient statistic the problem is solved. That is I have to use the Rao-Blackwell theorem, but I'm not exactly sure how that follows. I would appreciate any tips!

Given $m$ i.i.d. Bernoulli( $\theta$ ) r.v.s $X_{1}, X_{2}, \ldots, X_{m},$ I'm interested in finding the UMVUE of $(1-\theta)^{1/k}$, when $k$ is a positive integer. .

I know $\sum X_{i}$ is a sufficient statistic by the Factorization Theorem, but I'm having trouble proceeding from there. If I can find an unbiased function of the sufficient statistic the problem is solved by the Rao-Blackwell theorem.