To simplify the expression \( 13^{-5} \cdot 13^{-11} \), we can use the property of exponents that states \( a^m \cdot a^n = a^{m+n} \).
Applying this property:
\[ 13^{-5} \cdot 13^{-11} = 13^{-5 + (-11)} = 13^{-16} \]
Now we need to convert \( 13^{-16} \) into a form with only positive exponents. This can be done using the property that \( a^{-n} = \frac{1}{a^n} \):
\[ 13^{-16} = \frac{1}{13^{16}} \]
Among the choices provided, \( \frac{1}{13^{16}} \) is equivalent to:
1/13^16
So the answer is:
1/13^16