Advanced inverse cube-root changes

Optional extension

All quantities and constants of proportionality are positive. In the difference statement, the value at the smaller input exceeds the value at the larger input by \(5\).

The quantity \(y\) is inversely proportional to \(\sqrt[3]{x}\).

1. If \(y\) is halved, \(x\) becomes \(p\) times its original value; find \(p\).[2]
2. The difference between the values of \(y\) at \(x=8\) and \(x=27\) is \(5\). Express \(y\) in terms of \(x\).[2]