Apply the Properties of Integer Exponents to generate an equivalent expression to (5−3)6⋅ 51710−2%0D%0A(%0D%0A5%0D%0A−%0D%0A3%0D%0A)%0D%0A6%0D%0A⋅%0D%0A %0D%0A5%0D%0A17%0D%0A10%0D%0A−%0D%0A2%0D%0A with only positive exponents, then solve the expression. %0D%0A%0D%0AShow your work.%0D%0A%0D%0A(1 point)%0D%0A(5−3)6⋅ 51710−2=%0D%0A(%0D%0A5%0D%0A−%0D%0A3%0D%0A)%0D%0A6%0D%0A⋅%0D%0A %0D%0A5%0D%0A17%0D%0A10%0D%0A−%0D%0A2%0D%0A=%0D%0A

To simplify the expression \((5^{-3})^6 \cdot 5^{1710^{-2}}\) and express it with only positive exponents, we will apply the properties of exponents step by step.

1. **Simplify \((5^{-3})^6\)**:
\[
(5^{-3})^6 = 5^{-3 \cdot 6} = 5^{-18}
\]

2. **Simplify \(5^{1710^{-2}}\)**:
First, we interpret \(1710^{-2}\).
\[
1710^{-2} = \frac{1}{1710^2}
\]
Thus,
\[
5^{1710^{-2}} = 5^{\frac{1}{1710^2}} \text{ (We will leave it as is for now).}
\]

Now we have:
\[
5^{-18} \cdot 5^{1710^{-2}}
\]

3. **Combine the two expressions** using the property of exponents that states \(a^m \cdot a^n = a^{m+n}\):
\[
5^{-18 + \frac{1}{1710^2}}
\]

Now, we want to express this with only positive exponents. We can express \(5^{-18}\) as:
\[
\frac{1}{5^{18}}
\]

Thus, we rewrite the entire expression:
\[
5^{-18 + \frac{1}{1710^2}} = \frac{1}{5^{18 - \frac{1}{1710^2}}}
\]

4. **Final expression with only positive exponents**:
\[
\frac{1}{5^{18 - \frac{1}{1710^2}}}
\]

5. **Solving the expression**:
To find the exact numerical value, we can estimate \(1710^{-2}\):
\[
1710^2 = 2924100 \implies \frac{1}{1710^2} \approx 0
\]

Thus,
\[
\text{For practical calculations: } 18 - \frac{1}{1710^2} \approx 18
\]

Hence, we get:
\[
\frac{1}{5^{18}}
\]

This is our final answer.

### Summary
The equivalent expression with only positive exponents is:
\[
\frac{1}{5^{18 - \frac{1}{1710^2}}}
\]
And numerically simplified (as much as needed) it approximates to:
\[
\frac{1}{5^{18}}
\]