Express the following as the power of a rational number.
`(-32)/(3125)`

Answer

To express the fraction \((-32)/(3125)\) as the power of a rational number, we can follow these steps:

### Step 1: Factor the numerator and denominator
First, we need to factor both \(-32\) and \(3125\).

- **Numerator**:
\(-32\) can be expressed as:
\[ -32 = - (2^5) \]

- **Denominator**:
\(3125\) can be factored as:
\[ 3125 = 5^5 \]

### Step 2: Write the fraction using the factored forms
Now we can rewrite the original fraction using these factored forms:
\[ \frac{-32}{3125} = \frac{-2^5}{5^5} \]

### Step 3: Combine the fraction
We can express the fraction as:
\[ \frac{-2^5}{5^5} = -\left(\frac{2}{5}\right)^5 \]

### Step 4: Final expression
Thus, we can express \((-32)/(3125)\) as:
\[ -\left(\frac{2}{5}\right)^5 \]

### Conclusion
The final answer is:
\[ -\left(\frac{2}{5}\right)^5 \]

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