To simplify the expression \( 5^9 \cdot 5^{-13} \) using the properties of integer exponents, we can apply the product of powers property, which states that \( a^m \cdot a^n = a^{m+n} \).
Using this property:
\[ 5^9 \cdot 5^{-13} = 5^{9 + (-13)} = 5^{-4} \]
Now we want to express this with only positive exponents. To convert \( 5^{-4} \) to a positive exponent, we can use the property that \( a^{-n} = \frac{1}{a^n} \):
\[ 5^{-4} = \frac{1}{5^4} \]
Therefore, the equivalent expression to \( 5^9 \cdot 5^{-13} \) with only positive exponents is:
\[ \frac{1}{5^4} \]
Of the options provided, this is the same as the response:
\[ \text{Start Fraction 1 over 5 superscript 4 baseline end fraction} \]
So the correct answer is:
Start Fraction 1 over 5 superscript 4 baseline end fraction.