symbolic function with specific properties

I need to implement the symbolic function E(m(x)), where x = [x1, ..., xN] are symbolic variables, with the folowing property:

1. m(x) is monomial of x .... m(x) = x1^p1 * x2^p2 * ... * xN^pN, where pj >=0 ... integer power value, j = 1,2,...,N
2. E(m(x)) = E(x1^p1 * x2^p2 * ... * xN^pN) = E(x1^p1) * E(x2^p2) * ... * E(xN^pN)
3. E(c) = 0, where c is any other symbolic value

Examples:

E(x1^2*x2) = E(x1^2)*E(x2)
E(x1*x2^3*x3) = E(x1)*E(x2^3)*E(x3)
E(2) = 0
E(a*b) = 0
E(c^3) = 0

Any hints?