Summary: We introduce the power difference calculus based on the operator \(D_{n,q}f (t)=\frac{f(qt^n)-f(t)}{qt^n-t}\), where \(n\) is an odd positive integer and \(0<q<1\). Properties of the new operator and its inverse – the \(d_{n,q}\) integral – are proved. As an application, we consider power quantum Lagrangian systems and corresponding \(n,q\)-Euler-Lagrange equations.