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

Explanation

\(p^{\frac{1}{3}}\) = \(\frac{\sqrt[3]{q}}{r}\)

          cross multiply
\(p^{\frac{1}{3}}\) = \(\frac{q^{1/3}}{r}\)

r\(p^{\frac{1}{3}}\) =  \(q^{\frac{1}{3}}\)

take the cube of both sides

 \((rp^{\frac{1}{3}})^3\) =  \((q^{\frac{1}{3}})^3\)

\(r^3p^{\frac{3}{3}}\) = \(q^{\frac{3}{3}}\)

\(r^3\)p = q

 ∴ q = p\(r^3\)