`111 div [-5^(2) + (-4)` of `{33 div (-22 div -2)}]` =

Options

A. a) 37
B. `b)-5`
C. `c) -37`
D. `d) -3`

Answer

To solve the expression \( 111 \div [-5^2 + (-4) \cdot (33 \div (-22 \div -2))] \), we will follow the order of operations, commonly known as BODMAS/BIDMAS (Brackets, Orders, Division and Multiplication, Addition and Subtraction).

### Step-by-Step Solution:

1. **Calculate \( -22 \div -2 \)**:
\[ -22 \div -2 = 11 \]
**Hint**: Dividing two negative numbers gives a positive result.

2. **Substitute back into the expression**:
Now we replace \( -22 \div -2 \) with \( 11 \):
\[ 111 \div [-5^2 + (-4) \cdot (33 \div 11)] \]

3. **Calculate \( 33 \div 11 \)**:
\[ 33 \div 11 = 3 \]
**Hint**: Division of a number by itself results in 1, and dividing by a smaller number gives a larger quotient.

4. **Substitute back into the expression**:
Now we replace \( 33 \div 11 \) with \( 3 \):
\[ 111 \div [-5^2 + (-4) \cdot 3] \]

5. **Calculate \( -4 \cdot 3 \)**:
\[ -4 \cdot 3 = -12 \]
**Hint**: Multiplying a negative number by a positive number results in a negative product.

6. **Calculate \( -5^2 \)**:
\[ -5^2 = -25 \]
**Hint**: Remember that squaring a number always results in a positive value, but the negative sign in front makes it negative.

7. **Combine the results**:
Now we substitute back:
\[ 111 \div [-25 - 12] \]
This simplifies to:
\[ 111 \div [-37] \]

8. **Final division**:
\[ 111 \div -37 = -3 \]
**Hint**: Dividing a positive number by a negative number results in a negative quotient.

### Final Answer:
\[ \text{The final result is } -3. \]