By what number should `(-3) ^(-1)` be multiplied so that the proudct becomes `6 ^(-1)` ?

Options

A. `1/2`
B. `2/3`
C. `(-1)/2`
D. `(-2)/3`

Answer

To solve the problem, we need to find the number \( x \) such that:

\[ (-3)^{-1} \times x = 6^{-1} \]

### Step-by-Step Solution:

1. **Understand the equation**:
We start with the equation:
\[ (-3)^{-1} \times x = 6^{-1} \]

2. **Rewrite the negative exponents**:
Recall that \( a^{-n} = \frac{1}{a^n} \). Therefore, we can rewrite the equation as:
\[ \frac{1}{-3} \times x = \frac{1}{6} \]

3. **Isolate \( x \)**:
To isolate \( x \), we can multiply both sides by \(-3\):
\[ x = \frac{1}{6} \times (-3) \]

4. **Calculate the right side**:
Now, we compute the right side:
\[ x = \frac{-3}{6} \]

5. **Simplify the fraction**:
Simplifying \(\frac{-3}{6}\) gives:
\[ x = -\frac{1}{2} \]

### Final Answer:
Thus, the number that should be multiplied by \((-3)^{-1}\) to get \(6^{-1}\) is:
\[ \boxed{-\frac{1}{2}} \]