Fill in the blank to make equivalent rational expressions. (-4)/(v)=(square )/(3v^8)

## Step 1<br />The problem involves equivalent rational expressions. The goal is to find the value that should be placed in the square to make the two expressions equivalent.<br /><br />## Step 2<br />The given equation is \(-\frac{4}{v} = \frac{\square}{3v^8}\). To make these two expressions equivalent, the numerator of the second fraction must be 12 times the numerator of the first fraction.<br /><br />## Step 3<br />This is because the denominator of the second fraction is 12 times the denominator of the first fraction. Therefore, the numerator of the second fraction must be 12 times the numerator of the first fraction to maintain the equivalence.<br /><br />## Step 4<br />So, the numerator of the second fraction is \(-4 \times 12 = -48\).