`3- (2^3 - 2[3 - 16 -: 2]) = `

Options

A. `-15`
B. `-5`
C. `1`
D. `2`

Answer

To solve the expression \( 3 - (2^3 - 2[3 - 16 \div 2]) \), we will follow the order of operations (PEMDAS/BODMAS).

### Step-by-Step Solution:

1. **Calculate \( 2^3 \)**:
\[ 2^3 = 8 \]
**Hint**: Remember that \( a^b \) means \( a \) multiplied by itself \( b \) times.

2. **Calculate \( 16 \div 2 \)**:
\[ 16 \div 2 = 8 \]
**Hint**: Division should be performed before subtraction in the brackets.

3. **Substitute back into the expression**:
\[ 3 - (8 - 2[3 - 8]) \]

4. **Calculate \( 3 - 8 \)**:
\[ 3 - 8 = -5 \]
**Hint**: When subtracting a larger number from a smaller number, the result is negative.

5. **Substitute back**:
\[ 3 - (8 - 2 \times -5) \]

6. **Calculate \( 2 \times -5 \)**:
\[ 2 \times -5 = -10 \]
**Hint**: Multiplying a positive number by a negative number results in a negative product.

7. **Substitute back**:
\[ 3 - (8 + 10) \]

8. **Calculate \( 8 + 10 \)**:
\[ 8 + 10 = 18 \]
**Hint**: Adding two positive numbers results in a larger positive number.

9. **Substitute back**:
\[ 3 - 18 \]

10. **Calculate \( 3 - 18 \)**:
\[ 3 - 18 = -15 \]
**Hint**: Subtracting a larger number from a smaller number results in a negative number.

### Final Answer:
\[ \text{The final result is } -15. \]