Which of the following is an equivalent expression to 59⋅5−13 with only positive exponents that has been generated by applying the Properties of Integer Exponents?(1 point)

To simplify the expression \( 59 \cdot 5^{-13} \) using the properties of integer exponents, we can follow these steps:

1. **Combine the exponents**: When multiplying powers with the same base, we add the exponents.
\[
59 \cdot 5^{-13} = 5^{9 + (-13)} = 5^{9 - 13} = 5^{-4}
\]

2. **Convert to positive exponent**: To express this in terms of positive exponents, we use the property \( a^{-n} = \frac{1}{a^n} \):
\[
5^{-4} = \frac{1}{5^4}
\]

Now, looking through the response options, we can see:

- **595−13**: This is not simplified and still has negative exponents.
- **Start Fraction 5 superscript 9 baseline over 5 superscript negative 13 baseline End Fraction**: This is \( \frac{5^9}{5^{-13}} \), which simplifies to \( 5^{9 - (-13)} \) or \( 5^{22} \), which is not the same.
- **54**: This is \( 5^4 \), but originally we have \( 5^{-4} \), so this is not equivalent.
- **Start Fraction 1 over 5 superscript 22 baseline end fraction**: This is \( \frac{1}{5^{22}} \), which is not equivalent to our expression.
- **5 superscript 4 baseline**: This is \( 5^4 \).

None of the options provided are equal to \( \frac{1}{5^4} \) or \( 5^{-4} \), which is the correct equivalent expression.

However, since they expect an answer based on positive exponents, the equivalent expression with only positive exponents derived from the original expression can be stated as:

- \( 5^{-4} = \frac{1}{5^4} \) is the correct form that maintains the positive exponent format.

Since none of the options are \( \frac{1}{5^{4}} \), it appears there might be an error. But if one needs to state an equivalent conversation, it can be \( 5^{-4} \) interpreted as \( \frac{1}{5^4} \).

If we need to select from the options that best relates, "Start Fraction 1 over 5 superscript 22 baseline end fraction" is a distractor; it represents an entirely different value.

Therefore:
If forced to choose, answer doesn’t match original equation result properly; if \( \frac{1}{5^4} \) was an option, that should have been accepted as appropriate equivalent.

Thus, for conclusion:
- \( 5^{-4} \) converts accordingly provides results, no proper replacements present in given options.