Given that $p^{\frac{1}{3}}$ = $\frac{\sqrt[3]{q}}{r}$, make q the subject of the equation

Analyze the question: We are given p^(1/3) = (∛q)/r and must make q the subject.

Concept: To remove a cube root, cube both sides. Remember (a^(1/3))³ = a and (∛q)³ = q.

Solution:

1. Start with: p^(1/3) = ∛q / r
2. Multiply both sides by r: r·p^(1/3) = ∛q
3. Cube both sides: (r·p^(1/3))³ = q
4. Simplify: r³ · p = q

So q = pr³

Check: Take p = 8 and r = 2. Then p^(1/3) = 2, so ∛q / 2 = 2, which gives ∛q = 4 and q = 64. Using the formula: pr³ = 8 × 8 = 64 ✓.

Matching the options: The options appear to have lost their formatting. Option C, "pr3", is read as pr³, which matches our result. Option B, "p3r", would read as 3pr, which does not match.

Exam tip: When a variable sits inside a root, isolate the root first, then raise both sides to the power that cancels it (cube for a cube root, square for a square root). Also, when cubing a product, cube each factor: (r·p^(1/3))³ = r³·p.