Given that \(p^{\frac{1}{3}}\) = \(\frac{\sqrt[3]{q}}{r}\), make q the subject of the equation
A
q = p\(\sqrt{r}\)
B
q = p3r
C
q = pr3
D
q = pr\(\frac{1}{3}\)
Verified Correct Answer: C.
Step-by-Step Mathematical Solution
\(p^{\frac{1}{3}}\) = \(\frac{\sqrt[3]{q}}{r}\)
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\(r^3\)
Source: Myschool Past Questions Archive (Record #36868)