To simplify \( 4^{13} \div 3^{-5} \), we can first rewrite the division by a negative exponent:
\[ 4^{13} \div 3^{-5} = 4^{13} \times 3^{5} \]
Now we can express \( 4^{13} \) in terms of base \( 2 \):
\[ 4^{13} = (2^2)^{13} = 2^{26} \]
Now we can combine the two parts:
\[ 4^{13} \times 3^{5} = 2^{26} \times 3^{5} \]
So, the simplified expression is:
\[ 2^{26} \times 3^{5} \]