What is the result of the expression: (-3)² - [54/18(-5 + 3)] + [11 - (-2)²]?

To solve the expression ((-3)² - [54/18(-5 + 3)] + [11 - (-2)²]), it is essential to evaluate each component step-by-step.

1. Start with ((-3)²). The square of (-3) is (9).

2. Next, evaluate the term (-5 + 3). This simplifies to (-2).

3. Now, substitute (-2) back into the expression (\frac{54}{18(-2)}). First, calculate (54/18), which is (3). Now, substituting gives (3 \times (-2)), which results in (-6).

4. The combined expression now looks like this: (9 - (-6) + [11 - (-2)²]).

5. Next, calculate ((-2)²). This equals (4). Hence, the term (11 - 4) simplifies to (7).

6. Now we can put all components together: (9 - (-6) + 7). The subtraction of a negative becomes addition: (9 + 6 + 7\