To find the product of the expression \( \sqrt{81} \cdot \sqrt{16} \), we first calculate each square root individually:
- \( \sqrt{81} = 9 \)
- \( \sqrt{16} = 4 \)
Now we multiply these two results together:
\[ \sqrt{81} \cdot \sqrt{16} = 9 \cdot 4 = 36 \]
Thus, the product of the expression in simplest radical form is:
\[ \boxed{36} \]