Answer
$f(A+B)=a^{A+B}=a^{A}\cdot a^{B}=f(A)\cdot f(B)$
Work Step by Step
Given
$f(x)=a^{x}$...........$(1)$
Then
$f(A+B)= a^{A+B}$...........[from (1)]
$f(A+B)= a^{A}•a^{B}$........[by laws of exponents]
$f(A+B)= f(A)•f(B)$ ..........[by using (1)】
Hence Proved.
