JAMB - Mathematics (1998 - No. 3)

If \(b^3\) = \(a^{-2}\) and \(c^{\frac{1}{3}}\) = \(a^\frac{1}{2}\)b, express c in terms of a

a^{-\(\frac{1}{2}\)}

a^{\(\frac{1}{3}\)}

a^{\(\frac{3}{2}\)}

a^{\(\frac{2}{3}\)}

\(c^{\frac{1}{3}}\) = \(a^{\frac{1}{2}}\)b

b = \(a^{-2}\) and \(c^{\frac{1}{3}}\) = \(a^{\frac{1}{2}}\)b

b = \(a^{-\frac{2}{3}}\)

\(c^{\frac{1}{3}}\) = \(a^{\frac{1}{2}}\) x \(a^{-\frac{2}{3}}\) = \(a^{-\frac{1}{6}}\)

take the cube of both sides

c = (\(a^{-\frac{1}{6}})^3\) = \(a^{-\frac{1}{2}}\)