Powers in $l$-ary groups of a special form. I

The article deals with powers in polyadic groups of a special form, that is in polyadic groups with $l$-ary operation $\eta_{s,\sigma,k}$, that is called polyadic operation of a special form and is defined on Cartesian power of $A^k$ $n$-ary group $\langle A,\eta\rangle$ by substitution $\sigma\in\mathbf{S}_k$ and $n$-ary operation $\eta$.