1. **Problem:** Find the total number of elements in the power set of a set $A$ containing 15 elements. 2. **Formula:** The power set of a set with $n$ elements has $2^n$ elements. 3. **Explanation:** Each element can either be in or out of a subset, so for each of the 15 elements, there are 2 choices, giving $2^{15}$ subsets. 4. **Calculation:** $$2^{15} = 32768$$ 5. **Answer:** The total number of elements in the power set of $A$ is $2^{15}$. Note: The question count is 18 as there are 18 distinct problems listed, but only the first problem is solved here as per instructions.