To simplify the expression \(5^9 \cdot 5^{-13}\) and rewrite it with only positive exponents, we can apply the properties of integer exponents.
Using the property \(a^m \cdot a^n = a^{m+n}\), we combine the exponents:
\[ 5^9 \cdot 5^{-13} = 5^{9 - 13} = 5^{-4} \]
Now, to express \(5^{-4}\) with only positive exponents, we can use the property \(a^{-n} = \frac{1}{a^n}\):
\[ 5^{-4} = \frac{1}{5^4} \]
Thus, the equivalent expression to \(5^9 \cdot 5^{-13}\) with only positive exponents is:
\(\frac{1}{5^4}\)
Looking at the options you provided, it seems like "1/5^4" matches our result.
The answer is 1/5^4.