To simplify the expression \(4^{13} \cdot 3^{-5}\), we can first rewrite \(4^{13}\) in terms of a base of \(2\):
\[ 4^{13} = (2^2)^{13} = 2^{26} \]
Now, we substitute this back into the original expression:
\[ 4^{13} \cdot 3^{-5} = 2^{26} \cdot 3^{-5} \]
Since this expression is already in its simplest form, we can leave it as:
\[ \frac{2^{26}}{3^5} \]
Thus, the simplified form of \(4^{13} \cdot 3^{-5}\) is:
\[ \frac{2^{26}}{3^5} \]