if we define $F_n$ be the $n$th fibonacci number and $\varphi$ be golden number then can we say that
$2^{F_n} \in \Theta(2^{\varphi^n})$
or in other word
$2^{\frac{\varphi^n - (-\varphi)^{-n}}{\sqrt{5}}} \in \Theta(2^{\varphi^n})$
It's simple to show that $F_n \in \Theta(\varphi^n)$ but about above one I don't have any Idea