By What number should `(-30)^(-1)` be divided to get `6^(-1)` ?

Answer

To solve the problem "By what number should \((-30)^{-1}\) be divided to get \(6^{-1}\)?", we can follow these steps:

### Step-by-Step Solution:

1. **Set up the equation**:
Let the number we need to find be \(x\). According to the problem, we have:
\[ \frac{(-30)^{-1}}{x} = 6^{-1} \]

2. **Rearrange the equation**:
To isolate \(x\), we can multiply both sides of the equation by \(x\):
\[ (-30)^{-1} = x \cdot 6^{-1} \]

3. **Rewrite the negative exponents**:
Recall that \(a^{-1} = \frac{1}{a}\). Therefore, we can rewrite the equation as:
\[ \frac{1}{-30} = x \cdot \frac{1}{6} \]

4. **Multiply both sides by 6**:
To solve for \(x\), we can multiply both sides by 6:
\[ 6 \cdot \frac{1}{-30} = x \]

5. **Simplify the left side**:
Now, simplify the left side:
\[ x = \frac{6}{-30} \]

6. **Reduce the fraction**:
Simplifying \(\frac{6}{-30}\) gives:
\[ x = \frac{1}{-5} = -\frac{1}{5} \]

### Final Answer:
Thus, the number by which \((-30)^{-1}\) should be divided to get \(6^{-1}\) is:
\[ x = -\frac{1}{5} \]

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