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 there are $2$ choices per element, leading to $2^n$ subsets. 4. **Calculation:** For $n=15$, total subsets = $2^{15} = 32768$. 5. **Answer:** The total number of elements in the power set is $2^{15}$. **Final answer:** (a) $2^{15}$