`2 - (5 - 3^3[4 -: 2 + 1]) =`

Options

A. `-21`
B. `32`
C. `45`
D. `78`

Answer

To solve the expression \( 2 - (5 - 3^3[4 -: 2 + 1]) \), we will follow the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)).

### Step-by-Step Solution:

1. **Evaluate the expression inside the brackets**:
\[ 4 -: 2 + 1 \]
Here, the notation "-:" indicates division. So we first perform the division:
\[ 4 \div 2 = 2 \]
Now, we add 1:
\[ 2 + 1 = 3 \]
Therefore, the expression simplifies to:
\[ 4 -: 2 + 1 = 3 \]

2. **Substitute back into the original expression**:
Now we substitute this back into the expression:
\[ 2 - (5 - 3^3[3]) \]

3. **Calculate \(3^3\)**:
\[ 3^3 = 27 \]
So, we can rewrite the expression as:
\[ 2 - (5 - 27 \times 3) \]

4. **Perform the multiplication**:
\[ 27 \times 3 = 81 \]
Substitute this back into the expression:
\[ 2 - (5 - 81) \]

5. **Simplify the expression inside the parentheses**:
\[ 5 - 81 = -76 \]
Now, we can rewrite the expression:
\[ 2 - (-76) \]

6. **Subtracting a negative number**:
Subtracting a negative number is the same as adding:
\[ 2 + 76 = 78 \]

### Final Answer:
The final simplified expression is:
\[ \boxed{78} \]