Fill in the blank to make equivalent rational expressions.
\[
\frac{8}{3 w^{7}}=\frac{\square}{3 w^{9}}
\]

Step 1 ：First, we need to understand the problem. We are given two rational expressions and we need to find the value that makes them equivalent.

Step 2 ：The two expressions are equivalent if they are equal to each other. So, we can set up an equation to solve for the unknown value.

Step 3 ：The equation is: \(\frac{8}{3 w^{7}} = \frac{\square}{3 w^{9}}\)

Step 4 ：We can simplify this equation by multiplying both sides by \(3 w^{9}\) to get rid of the denominator on the right side.

Step 5 ：After multiplying, we get: \(8 w^{2} = \square\)

Step 6 ：So, the value that makes the two expressions equivalent is \(8 w^{2}\)

Step 7 ：Finally, we check our solution by substituting \(8 w^{2}\) into the original equation. We find that the two sides are indeed equal, so our solution is correct.

Step 8 ：Therefore, the final answer is \(\boxed{8 w^{2}}\)