IP1U1 SWII Q14

The number \(1728\) written as a product of its prime factors is \(1728 = 2^{6} \times 3^{3}\).

Using only the above result and showing your working clearly, find

1. the smallest positive integer value of \(k\) for which \(1728k\) is a square number,
2. an expression in terms of \(x\) for \(\sqrt[3]{1728x^9}\).