Find the value of `(3x)^(215)`, if `x= -1"/"3`.

Options

A. `1`
B. `-1`
C. `215`
D. `645`

Answer

To find the value of \((3x)^{215}\) given that \(x = -\frac{1}{3}\), we can follow these steps:

### Step-by-Step Solution:

1. **Substitute the value of \(x\)**:
\[ (3x)^{215} = (3 \cdot -\frac{1}{3})^{215} \]

2. **Simplify the expression inside the parentheses**:
\[ 3 \cdot -\frac{1}{3} = -1 \]
So, we have:
\[ (3x)^{215} = (-1)^{215} \]

3. **Evaluate \((-1)^{215}\)**:
Since 215 is an odd number, we know that:
\[ (-1)^{\text{odd}} = -1 \]
Therefore:
\[ (-1)^{215} = -1 \]

4. **Final Answer**:
\[ (3x)^{215} = -1 \]