The exponential function $f(x) = a^x$ passes through the point $(3, 125)$. To find the value of $a$, we can substitute the point $(3, 125)$ into the function.

1. The function is $f(x) = a^x$.
2. Substituting $x = 3$ and $f(3) = 125$, we get: $125 = a^3$
3. Solving for $a$, we take the cube root of both sides: $a = \sqrt[3]{125}$ $a = 5$

Thus, the value of $a$ is $5$, and the exponential function is: $f(x) = 5^x$

Would you like more details or have any questions?

Here are some related questions:

1. How do you solve exponential equations with different bases?
2. What is the general form of an exponential function?
3. How do exponential functions relate to logarithms?
4. How do transformations affect the graph of an exponential function?
5. How can you determine the asymptote of an exponential function?

Tip: To find the base of an exponential function, plug in known points and solve using properties like roots or logarithms.