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Diophantine problems involving recurrence sequences have a long history andis an actively studied topic within number theory. In this paper, we connect tothe field by considering the equation \begin{align*} B_mB_{m+d}\dotsB_{m+(k-1)d}=y^\ell \end{align*} in positive integers $m,d,k,y$ with$\gcd(m,d)=1$ and $k\geq 2$, where $\ell\geq 2$ is a fixed integer and$B=(B_n)_{n=1}^\infty$ is an elliptic divisibility sequence, an important classof non-linear recurrences. We prove that the above equation admits onlyfinitely many solutions. In fact, we present an algorithm to find all possiblesolutions, provided that the set of $\ell$-th powers in $B$ is given. (Notethat this set is known to be finite.) We illustrate our method by an example.

Perfect powers in products of terms of elliptic divisibility sequences