Let $A = \{x,y,z\}$ and $B = \{1,2,3\}$.
The power set of $A$ is $$ P(A) = \{∅, \{x\}, \{y\}, \{z\}, \{x, y\}, \{x, z\}, \{y, z\}, \{x, y, z\}\}. $$
When working out the Cartesian product for example $A \times B$ you simply order the pairs in which the first element comes from A and the second elements come from B.
A x B = {$(x,1),(x,2),(x,3),(y,1),(y,2),(y,3),(z,1),(z,2),(z,3)$}
B x A = {$(1,x),(1,y)...(3,z)$}
For the Cartesian product $P(A)\times A$ you can not create a list of ordered pairs as $P(A)$ has a list of lists and $A$ has a list of elements. Is there a way to find the Cartesian product of $P(A)\times A$?
The set would consist of $$P(A)\times A = \{(a, b)\mid a\in P(A) \land b \in A\}$$ That is, the ordered pair consists of (set (element) in $P(A)$, element in $A$).
$$P(A)\times A = \{(\varnothing, x), (\varnothing, y), (\varnothing, z), (\{x\}, x), \ldots (\{y\}, x), \ldots (\{x, y, z\}, z)\}$$