`77 div [46 - {66 - (52 - 63 div 9 xx 3)}] = ?`

Options

A. 5
B. 6
C. 11
D. 7

Answer

To solve the expression \( 77 \div [46 - \{66 - (52 - 63 \div 9 \times 3)\}] \), we will follow the BODMAS/BIDMAS rule, which stands for Brackets, Orders (i.e., powers and roots, etc.), Division and Multiplication (from left to right), Addition and Subtraction (from left to right).

### Step-by-step Solution:

1. **Identify the innermost bracket**: Start with the expression inside the round brackets: \( 63 \div 9 \times 3 \).

- **Hint**: Always start with the innermost brackets when using BODMAS.

2. **Perform the division**: Calculate \( 63 \div 9 \).
\[ 63 \div 9 = 7 \]

- **Hint**: Remember to perform division before multiplication.

3. **Substitute back into the expression**: Now replace \( 63 \div 9 \) with \( 7 \) in the expression:
\[ 52 - 7 \times 3 \]

4. **Perform the multiplication**: Calculate \( 7 \times 3 \).
\[ 7 \times 3 = 21 \]

- **Hint**: After division, the next step is to perform multiplication.

5. **Substitute back into the expression**: Now replace \( 7 \times 3 \) with \( 21 \):
\[ 52 - 21 \]

6. **Perform the subtraction**: Calculate \( 52 - 21 \).
\[ 52 - 21 = 31 \]

- **Hint**: After resolving the innermost brackets, move outward and perform the operations.

7. **Substitute back into the expression**: Now replace \( (52 - 63 \div 9 \times 3) \) with \( 31 \):
\[ 77 \div [46 - \{66 - 31\}] \]

8. **Calculate \( 66 - 31 \)**:
\[ 66 - 31 = 35 \]

- **Hint**: Continue resolving the brackets from the innermost to the outermost.

9. **Substitute back into the expression**: Now replace \( \{66 - 31\} \) with \( 35 \):
\[ 77 \div [46 - 35] \]

10. **Calculate \( 46 - 35 \)**:
\[ 46 - 35 = 11 \]

- **Hint**: Keep simplifying the expression until you reach a single value.

11. **Final division**: Now perform the division:
\[ 77 \div 11 = 7 \]

- **Hint**: The last operation is the division, which gives you the final answer.

### Final Answer:
\[ \text{The answer is } 7. \]