(1) If f(x) = a^x, show that f(A + B) = f(A) * f(B)
(2) If f(x) = a^x, show that f(Ax) = [f(x)]^A
(1) $\displaystyle f(x)~=~a^x $
$\displaystyle \implies~f(A)~=~a^A~,$
$\displaystyle ~f(B)~=~a^B~,$
$\displaystyle ~f(A+B)~=~a^{A+B}~=~a^A \cdot a^B~=~f(A) \cdot f(B)$
(2) $\displaystyle f(x)~=~a^x$
$\displaystyle \implies~f(Ax)~=~a^{Ax}~=~(a^x)^A~=~[f(x)]^A$