How to write $A\cup\emptyset\times A\cup\emptyset$

Question

How to write the cartesian product of this?

$$(A\cup\emptyset)\times (A\cup\emptyset)$$

Is it: $$A^2\cup\emptyset^2?$$

What does $\emptyset^n$ means?

Answer 1

HINT: Note that $X\cup\varnothing=X$. Also, note that generally $(A\cup B)^2\neq A^2\cup B^2$, much like $(x+y)^2\neq x^2+y^2$.