What is the coefficient of the fourth term in this expression?

To find the coefficient of the fourth term in the expression \( 4u^2 + 9 + 8v + v^3 \), we first need to identify the terms in the expression.

1. The first term is \( 4u^2 \).
2. The second term is \( 9 \).
3. The third term is \( 8v \).
4. The fourth term is \( v^3 \).

Now, we need to determine the coefficient of the fourth term, which is \( v^3 \). The coefficient of \( v^3 \) is simply the number in front of \( v^3 \).

In this case, the coefficient of the fourth term \( v^3 \) is \( 1 \) (since there is no number explicitly written in front of \( v^3 \), it is understood to be \( 1 \)).

Therefore, the coefficient of the fourth term is:

\[ \boxed{1} \]