To simplify the expression \( \frac{4^{13}}{3^{-5}} \), we can use the property of exponents that states \( a^{-n} = \frac{1}{a^n} \).
First, we rewrite \( 3^{-5} \):
\[ 3^{-5} = \frac{1}{3^5} \]
Now substituting this into the expression gives:
\[ \frac{4^{13}}{3^{-5}} = 4^{13} \cdot 3^5 \]
Now we can write the final simplified expression:
\[ 4^{13} \cdot 3^5 \]
There are no further simplifications that can be made unless numerical values are needed. This is the simplified form of the original expression:
\[ 4^{13} \cdot 3^5 \]