To simplify \( 4^{13} \div 3^{-5} \), we can rewrite the expression using the property of exponents \( a^{-b} = \frac{1}{a^{b}} \).
Starting with the expression:
\[ 4^{13} \div 3^{-5} \]
This can be rewritten as:
\[ 4^{13} \times 3^{5} \]
Now, we simply compute the values separately.
First, let's compute \( 4^{13} \). We know that \( 4 = 2^2 \), so:
\[ 4^{13} = (2^2)^{13} = 2^{26} \]
Next, we have \( 3^{5} \).
Putting it all together, we have:
\[ 4^{13} \times 3^{5} = 2^{26} \times 3^{5} \]
Thus, the expression simplifies to:
\[ 2^{26} \times 3^{5} \]
This is the simplified form of \( 4^{13} \div 3^{-5} \).
The numerical value can be calculated, but the expression itself is effectively simplified as \( 2^{26} \times 3^{5} \).