To make \(q\) the subject of the formula, we isolate \(q\) on one side of the equation.

Given equation: \(\frac{mn}{a^2} - \frac{pq}{b^2} = 1\)

Step 1: Add \(\frac{pq}{b^2}\) to both sides of the equation to move it to the right-hand side:

\(\frac{mn}{a^2} = 1 + \frac{pq}{b^2}\)

Step 2: Subtract 1 from both sides of the equation:

\(\frac{mn}{a^2} - 1 = \frac{pq}{b^2}\)

Step 3: Now, we need to make \(q\) the subject, so isolate \(q\) on the right-hand side:

\(\frac{pq}{b^2} = \frac{mn}{a^2} - 1\)

Step 4: To get \(q\) alone, multiply both sides by \(\frac{b^2}{p}\):

\(q = \frac{b^2(mn - a^2)}{a^2p}\)