To simplify the expression \(\sqrt{81} \cdot \sqrt{16}\), we can use the property of square roots that states:
\[ \sqrt{a} \cdot \sqrt{b} = \sqrt{a \cdot b} \]
Applying this property to our expression gives:
\[ \sqrt{81} \cdot \sqrt{16} = \sqrt{81 \cdot 16} \]
Now, we can calculate \(81 \cdot 16\):
\[ 81 \cdot 16 = 1296 \]
Next, we find \(\sqrt{1296}\). We can determine this by recognizing that:
\[ 1296 = 36^2 \]
Thus, we can take the square root:
\[ \sqrt{1296} = 36 \]
Therefore, we conclude:
\[ \sqrt{81} \cdot \sqrt{16} = 36 \]
In simplest radical form, the product of the expression is:
\[ \boxed{36} \]
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