The expression provided in the image is:

$-2^4 + 3^2 - 2 \cdot (-2)$

Step-by-Step Solution:

1. Evaluate the exponents first (according to the order of operations):

   • $2^4 = 16$
   • $3^2 = 9$

   Substitute these values back into the expression: $-(16) + 9 - 2 \cdot (-2)$

2. Simplify the multiplication:

   • $-2 \cdot (-2) = 4$

   The expression becomes: $-16 + 9 + 4$

3. Simplify the addition and subtraction:

   • $-16 + 9 = -7$
   • $-7 + 4 = -3$

Final Answer:

$\boxed{-3}$

Let me know if you'd like additional clarification or have any questions!

Questions to Expand Your Understanding:

1. How would the result change if the negative sign before $2^4$ was omitted?
2. What is the impact of parentheses in changing the order of operations here?
3. Can you rewrite this expression in a different order but still calculate the same result?
4. What happens if you replace $-2$ in the multiplication with another negative number?
5. Can you generalize a similar expression and test if the steps remain valid?

Tip: Always remember to follow the order of operations: parentheses, exponents, multiplication/division (left to right), addition/sub