`3[32-:8xx52-:(4+9)]=?`

Options

A. 19
B. 20
C. 21
D. 48

Answer

To solve the expression \( 3[32 -: 8 \times 52 -: (4 + 9)] \), we will follow the order of operations, often remembered by the acronym BODMAS/BIDMAS (Brackets, Orders, Division and Multiplication, Addition and Subtraction).

### Step-by-Step Solution:

1. **Identify the Expression**:
The expression can be rewritten for clarity as:
\[ 3 \left[ \frac{32}{8} \times \frac{52}{(4 + 9)} \right] \]

2. **Calculate Inside the Brackets**:
First, we need to solve the expression inside the brackets. Start with the addition:
\[ 4 + 9 = 13 \]
Now we can substitute this back into the expression:
\[ 3 \left[ \frac{32}{8} \times \frac{52}{13} \right] \]

3. **Perform the Division**:
Now, calculate \( \frac{32}{8} \):
\[ \frac{32}{8} = 4 \]
Next, calculate \( \frac{52}{13} \):
\[ \frac{52}{13} = 4 \]
Now, substitute these values back into the expression:
\[ 3 \left[ 4 \times 4 \right] \]

4. **Multiply Inside the Brackets**:
Now, multiply the values inside the brackets:
\[ 4 \times 4 = 16 \]
Substitute this back into the expression:
\[ 3 \times 16 \]

5. **Final Multiplication**:
Finally, multiply:
\[ 3 \times 16 = 48 \]

Thus, the value of the expression \( 3[32 -: 8 \times 52 -: (4 + 9)] \) is \( \boxed{48} \).