To solve this problem, we'll need to carefully consider the placement of parentheses and the order of operations when dealing with negative numbers and exponentiation:
- Step 1: Examine the given expression (−4)2. This indicates squaring the entire negative four, which results in 16.
- Step 2: Now, examine −(−4)2 paying close attention to the negative sign in front. (−4)2 again results in 16, but placing a minus before it changes its sign to −16.
Let's analyze each possible choice:
- For choice 1: The expression is −(−4)2. Calculating (−4)2 gives 16, and applying the negative sign outside results in the expression value of −16.
- For choice 2: The expression is (−4)2, calculated to give 16.
Therefore, the expression that correctly equals −16 is choice 1, represented by −(−4)2.
The correct answer is choice 1: −(−4)2.