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) Responses 54 5 superscript 4 baseline 1522 Start Fraction 1 over 5 superscript 22 baseline end fraction 154 Start Fraction 1 over 5 superscript 4 baseline end fraction 595−13

To simplify the expression \(59 \cdot 5^{-13}\) using the properties of integer exponents, we can rewrite it as follows:

Using the property \(a^{-n} = \frac{1}{a^n}\):

\[
59 \cdot 5^{-13} = 59 \cdot \frac{1}{5^{13}} = \frac{59}{5^{13}}
\]

Now we can analyze the options given:

1. \(54\) - This is just a number, not equivalent.
2. \(5^4 \cdot 1522\) - This does not match our form.
3. \(\frac{1}{5^{22}}\) - This does not match our form.
4. \(5^4 \cdot 154\) - Incorrect form.
5. \(\frac{1}{5^4}\) - This is not equivalent.
6. \(59 \cdot 5^{-13}\) - This is not transformed to positive exponents.

None of these mentions match the simplified form \(\frac{59}{5^{13}}\) directly, but we realize that the question asks for an equivalent expression in a different format, where the expression maintains the property of having only positive exponents.

If we look at the expression obtained \(59 \cdot 5^{-13} = \frac{59}{5^{13}}\), it can only be rewritten differently:

The best equivalent expression that uses only positive exponents would be:

\[
\frac{59}{5^{13}} \text{ which may not directly appear among your given choices but think about evaluations or options in tests.}
\]

Since none of the presented choices match the full simplified expression of \(\frac{59}{5^{13}}\) or show any transformation based on \(n\) times anything that sums it up directly, you would select the one that seems to align most closely with the format you've learned or the expressions that embody negative exponents transformed back. Please double-check what is exactly provided in your questions against fully termed explications in your references.