The value of `(-2)^(2xx3-1)` is

Options

A. 32
B. 64
C. `-32`
D. `-64`

Answer

To solve the expression \((-2)^{(2 \times 3 - 1)}\), we will follow the order of operations (BODMAS/BIDMAS) which stands for Brackets, Orders (i.e., powers and roots, etc.), Division and Multiplication, Addition and Subtraction.

### Step-by-Step Solution:

1. **Calculate the expression inside the exponent**:
\[ 2 \times 3 - 1 \]
- First, perform the multiplication:
\[ 2 \times 3 = 6 \]
- Then, subtract 1 from 6:
\[ 6 - 1 = 5 \]

2. **Rewrite the expression**:
Now we can rewrite the original expression with the calculated exponent:
\[ (-2)^{5} \]

3. **Calculate \((-2)^{5}\)**:
- When raising \(-2\) to the power of 5, we multiply \(-2\) by itself five times:
\[ (-2) \times (-2) \times (-2) \times (-2) \times (-2) \]
- First, calculate \((-2) \times (-2)\):
\[ (-2) \times (-2) = 4 \]
- Next, multiply the result by \(-2\):
\[ 4 \times (-2) = -8 \]
- Now, multiply \(-8\) by \(-2\):
\[ -8 \times (-2) = 16 \]
- Finally, multiply \(16\) by \(-2\):
\[ 16 \times (-2) = -32 \]

4. **Final Result**:
Therefore, the value of \((-2)^{(2 \times 3 - 1)}\) is:
\[ \boxed{-32} \]