  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.
