To simplify the expression \(\frac{4^{12} \cdot 4^{8}}{4^{13}}\), we can use the properties of exponents.
First, we can simplify the numerator, \(4^{12} \cdot 4^{8}\), using the rule \(a^m \cdot a^n = a^{m+n}\):
\[ 4^{12} \cdot 4^{8} = 4^{12 + 8} = 4^{20} \]
Now, the expression becomes:
\[ \frac{4^{20}}{4^{13}} \]
Next, we apply the rule \(\frac{a^m}{a^n} = a^{m-n}\):
\[ \frac{4^{20}}{4^{13}} = 4^{20 - 13} = 4^{7} \]
Thus, the simplified result is:
\[ \boxed{4^7} \]