Express the following as a rational number.
`((-3)/(5))^(3)`

Answer

To express \((-3/5)^3\) as a rational number, follow these steps:

### Step 1: Write the expression
We start with the expression:
\[ \left(-\frac{3}{5}\right)^3 \]

### Step 2: Apply the exponent
When raising a fraction to a power, we can apply the exponent to both the numerator and the denominator:
\[ \left(-\frac{3}{5}\right)^3 = \frac{(-3)^3}{(5)^3} \]

### Step 3: Calculate the numerator
Now, calculate \((-3)^3\):
\[ (-3)^3 = -3 \times -3 \times -3 = -27 \]

### Step 4: Calculate the denominator
Next, calculate \(5^3\):
\[ 5^3 = 5 \times 5 \times 5 = 125 \]

### Step 5: Combine the results
Now, we can combine the results from the numerator and denominator:
\[ \left(-\frac{3}{5}\right)^3 = \frac{-27}{125} \]

### Step 6: Final expression as a rational number
Thus, the expression \((-3/5)^3\) as a rational number is:
\[ -\frac{27}{125} \]

### Summary
The final answer is:
\[ -\frac{27}{125} \]

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