To simplify the expression \( 13^{-5} \cdot 13^{-11} \) and express it using only positive exponents, we can apply the properties of exponents.
Using the property that \( a^m \cdot a^n = a^{m+n} \), we combine the exponents:
\[ 13^{-5} \cdot 13^{-11} = 13^{-5 + (-11)} = 13^{-16} \]
To express this with only positive exponents, we use the property \( a^{-n} = \frac{1}{a^n} \):
\[ 13^{-16} = \frac{1}{13^{16}} \]
Now, looking at the provided options, the equivalent expression is:
\(\frac{1}{13^{16}}\)
So the correct equivalent expression is:
1/1316 Start Fraction 1 over 13 Superscript 16 baseline End Fraction