The power set $P(A)$ of a set $A$ is the set of all subsets of $A$, including the empty set and $A$ itself.

Now, let's go through the process for the empty set:

1. Let the empty set be denoted as $\emptyset$, which is a set containing no elements.
2. The power set of $\emptyset$ is the set of all subsets of $\emptyset$.
3. The only subset of the empty set is the empty set itself.

Therefore, the power set of the empty set is:

$P(\emptyset) = \{ \emptyset \}$

So, the power set of the empty set contains one element, which is the empty set.

Do you want further details or have any questions?

Here are 5 questions to expand on this concept:

1. What is the power set of a set with one element, such as $A = \{a\}$?
2. How many elements does the power set of a set with $n$ elements contain?
3. What is the relationship between the cardinality of a set and its power set?
4. Can a power set itself be empty? Why or why not?
5. How would you compute the power set of $A = \{1, 2\}$?

Tip: The power set of a set with $n$ elements always contains $2^n$ subsets.