Vector to Multi-Index Exponential

Operation

For vector $v=(x,y,z,\dots )$ $v^{(x_1,x_2,\dots )}=x^{x_1}{y}^{x_2}{z}^{x_3}\dots$

Example

In ${\mathbb{R}}^4$ with the vector $v=(x,y,z,w)$ For the Multi-Index $(1,0,2,3)$ $v^{(1,0,2,3)}=x^1{y}^0{z}^2{w}^3$