Answer
False.
Replace "$ f(a)+f(b)$" with "$ f(a)\cdot f(b)$"
Work Step by Step
$ f(a+b)=2^{a+b}=2^{a}\cdot 2^{b}=f(a)\cdot f(b)$
So, the statement is false.
The simplest way to make it true is to replace "$ f(a)+f(b)$" with "$ f(a)\cdot f(b)$"
