To simplify the expression \( \frac{4^{13}}{3^{-5}} \), we can start by recalling that dividing by a negative exponent is equivalent to multiplying by the positive exponent:
\[ \frac{4^{13}}{3^{-5}} = 4^{13} \cdot 3^{5} \]
Now, we can express it as:
\[ 4^{13} \cdot 3^{5} \]
At this point, there isn't a standard way to simplify \( 4^{13} \cdot 3^{5} \) further without calculating the actual numerical values. However, if you need it in terms of powers, it can just remain as:
\[ 4^{13} \cdot 3^{5} \]
If you would like to calculate the numerical value:
- Calculate \( 4^{13} \).
- Calculate \( 3^{5} \).
- Multiply the two results.
Calculating these:
- \( 4^{13} = 67,108,864 \)
- \( 3^{5} = 243 \)
So,
\[ 4^{13} \cdot 3^{5} = 67,108,864 \cdot 243 = 16,349,249,152 \]
Thus, the simplified expression is either \( 4^{13} \cdot 3^{5} \) or its numerical value \( 16,349,249,152 \).