Solve (-(-2)²)² - 2³: Multiple Exponents and Negative Numbers

$(-(-2)^2)^2-2^3=$

To solve this problem, we need to carefully apply the order of operations, commonly known as PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).
Let's evaluate the expression step-by-step:

• Step 1: Begin with the expression inside the innermost parentheses: $(-2)^2$. This means we first square $-2$, which results in $4$ because $(-2) \times (-2) = 4$.
• Step 2: Now, consider the negative sign outside the squared term. So, evaluate $-(-2)^2$, which simplifies to $-4$.
• Step 3: Next, we need to square $-4$: $(-4)^2 = (-4) \times (-4) = 16$.
• Step 4: Now, calculate the second part of the expression, $2^3$, which equals $8$ because $2 \times 2 \times 2 = 8$.
• Step 5: Finally, subtract the result from Step 4 from the result of Step 3: $16 - 8 = 8$.

Thus, the solution to the problem is $8$.