Solve -(-2)^4+(-2)^2: Order of Operations with Negative Exponents

To solve this problem, let's evaluate the expression $-(-2)^4 + (-2)^2$ step-by-step:

• Step 1: Calculate $(-2)^4$.
  Since the exponent is even, $(-2)^4 = ((-2) \times (-2) \times (-2) \times (-2))$.
  Calculating more explicitly:
  $(-2) \times (-2) = 4$,
  $4 \times (-2) = -8$,
  $-8 \times (-2) = 16$.
  Thus, $(-2)^4 = 16$.

• Step 2: Negate the result from step 1.
  $-(-2)^4 = -(16) = -16$.

• Step 3: Calculate $(-2)^2$.
  Since the exponent is even, $(-2)^2 = (-2) \times (-2) = 4$.

• Step 4: Add the results from step 2 and step 3.
  $-16 + 4 = -12$.

Therefore, the final result is $\mathbf{-12}$.