Chapter 5 - Exponential and Logarithmic Functions - 5.3 Exponential Functions - 5.3 Assess Your Understanding - Page 285: 125

\begin{align*} f(A+B)&=a^{A+B}=a^A\cdot a^B=f(A)\cdot f(B) \end{align*}

If $f(x)=a^x$, then: $f(A)=a^A\text{ and } f(B)=a^B$ Substitute $A+B$ to $x$ to obtain: \begin{align*} f(A+B)&=a^{A+B}\\ &=a^A\cdot a^B\\ &=f(A)\cdot f(B) \end{align*}