Which of the following is an equivalent expression to \( 13^{-5} \cdot 13^{-11} \) with only positive exponents, generated by applying the properties of exponents? (1 point) \( \frac{1}{13^{16}} \) \( \frac{1}{26^{6}} \) \( \frac{1}{13^{6}} \) \( \frac{1}{26^{16}} \)

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: \[ 13^{-5} \cdot 13^{-11} = 13^{-5 + (-11)} = 13^{-16} \] Next, we want to express \( 13^{-16} \) with only positive exponents. We can do this by using the property that \( a^{-n} = \frac{1}{a^n} \): \[ 13^{-16} = \frac{1}{13^{16}} \] Thus, the equivalent expression to \( 13^{-5} \cdot 13^{-11} \) with only positive exponents is: \[ \frac{1}{13^{16}} \] Among the options provided, the correct answer is: \(\frac{1}{13^{16}}\) (Note: This option is not listed, but the correct simplification is indeed \(\frac{1}{13^{16}}\)). If we consider the options given, the closest correct answer based on the simplification is: \(\frac{1}{13^{16}}\) (if it were listed). However, since it is not listed, we can conclude that the answer is not present in the options provided.