Fill in the blank to make equivalent rational expressions. \( \frac{7}{3 y}=\frac{\square}{18 y^{7}} \)

To find the missing value, we can cross-multiply. We set up the equation as follows: \( 7 \cdot 18 y^{7} = 3 y \cdot \square \) This simplifies to: \( 126 y^{7} = 3 y \cdot \square \) To isolate \(\square\), divide both sides by \(3y\): \(\square = \frac{126 y^{7}}{3y}\) When you simplify \(\frac{126}{3}\), you get \(42\). Therefore, the missing value is: \(42y^{6}\) So the complete expression is: \( \frac{7}{3 y}=\frac{42y^{6}}{18 y^{7}} \).