WAEC - Mathematics (2013 - No. 13)
Given that \(p^{\frac{1}{3}}\) = \(\frac{\sqrt[3]{q}}{r}\), make q the subject of the equation
q = p\(\sqrt{r}\)
q = p3r
q = pr3
q = pr\(\frac{1}{3}\)
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\(r^3\)
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