To simplify the expression \( 13^{-5} \cdot 13^{-11} \) using the properties of exponents, we can apply the property that states \( a^m \cdot a^n = a^{m+n} \).
Here, we have: \[ 13^{-5} \cdot 13^{-11} = 13^{-5 + (-11)} = 13^{-16} \]
Since we want an expression with only positive exponents, we can rewrite \( 13^{-16} \) as: \[ 13^{-16} = \frac{1}{13^{16}} \]
Among the given options, \( \frac{1}{13^{16}} \) corresponds to the choice:
11316 Start Fraction 1 over 13 Superscript 16 baseline end fraction
Therefore, the equivalent expression is: \[ \boxed{\frac{1}{13^{16}}} \]