Find the cube - roots of :
`-27/343`

Answer

To find the cube roots of \(-\frac{27}{343}\), we will follow these steps:

### Step 1: Factor the numerator and denominator
First, we factor the numerator and denominator:
- The numerator \(27\) can be expressed as \(3^3\) because \(27 = 3 \times 3 \times 3\).
- The denominator \(343\) can be expressed as \(7^3\) because \(343 = 7 \times 7 \times 7\).

### Step 2: Rewrite the fraction
Now we can rewrite the fraction:
\[ -\frac{27}{343} = -\frac{3^3}{7^3} \]

### Step 3: Simplify the fraction
This can be simplified to:
\[ -\frac{3^3}{7^3} = -\left(\frac{3}{7}\right)^3 \]

### Step 4: Find the cube root
To find the cube root of \(-\frac{27}{343}\), we take the cube root of both sides:
\[ \sqrt[3]{-\frac{27}{343}} = \sqrt[3]{-\left(\frac{3}{7}\right)^3} \]

### Step 5: Apply the cube root
Using the property of cube roots, we have:
\[ \sqrt[3]{-\left(\frac{3}{7}\right)^3} = -\frac{3}{7} \]

### Final Answer
Thus, the cube root of \(-\frac{27}{343}\) is:
\[ -\frac{3}{7} \]

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