  Let $\{ {U_{n}\}_{n \geq 0} }$ be a non-degenerate binary recurrence sequence
with positive discriminant. Let $\{p_1,\ldots, p_s\}$ be fixed prime numbers
and $\{b_1,\ldots ,b_s\}$ be fixed non-negative integers. In this paper, we
obtain the finiteness result for the solution of the Diophantine equation
$U_{n_{1}} + \cdots + U_{n_{t}} = b_1 p_1^{z_1} + \cdots+ b_s p_s^{z_s}
  $ under certain assumptions. Moreover, we explicitly solve the equation
$F_{n_1}+ F_{n_2}= 2^{z_1} +3^{z_2}$, in non-negative integers $n_1, n_2, z_1,
z_2$ with $z_2\geq z_1$. The main tools used in this work are the lower bound
for linear forms in logarithms and the Baker-Davenport reduction method.
