Given that p\(\frac{1}{3}\) = \(\frac{3\sqrt{q}}{r}\), make q the subject of the equation

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

Answer Details

We want to solve for q, so we need to isolate it on one side of the equation. First, we can isolate the cube root of p by cubing both sides of the equation: p^(1/3) = (3√q)/r (p^(1/3))³ = (3√q)³/r³ p = (27q)/r³ Next, we can isolate q by multiplying both sides by r³/27: (p/27)r³ = q Therefore, the solution is q = (p/27)r³, which is equivalent to q = pr^(1/3).