Powers of Fibonacci numbers which are products of repdigits

In this article we solve the equation F-n(k)= (d(1) <middle dot> 10(m)-1/9) <middle dot> (d(2) <middle dot> 10(q)-1/9), with n, k, d(1), d(2), m, q &is an element of N, d(1), d(2) = 1, ..., 9, m, q >= 2, k >= 2, 9 9 showing that the only perfect power of a Fibonacci number which is a product of two repdigits is F-10(2) = 55 <middle dot> 55.In order to do this we use only elementary methods, like divisibility properties of Fibonacci numbers, periodicity, results on prime factorizations and an application of Nagell-Ljunggren equations.