(a) Prove that \(2^{\frac{1}{3}}\) and \(3^{\frac{1}{3}}\) are irrational.

(b) Let \(m\) and \(n\) be positive integers. Prove that \(m^{\frac{1}{n}}\) is rational if and only if \(m\) is an \(n^{\text {th }}\) power (i.e., \(m=c^{n}\) for some integer \(c\) ).