The payoff of a power option is (hleft(S_{T} ight)), where the function (h) is given by (h(x)=x^{beta}(x-K)^{+}).

The payoff of a power option is \(h\left(S_{T}\right)\), where the function \(h\) is given by \(h(x)=x^{\beta}(x-K)^{+}\). Prove that the payoff can be written as the difference of European payoffs on the underlying assets \(S^{\beta+1}\) and \(S^{\beta}\) with strikes depending on \(K\) and \(\beta\).