Evaluate `root3((-64)/(125))`

Answer

To evaluate \( \sqrt[3]{\frac{-64}{125}} \), we can follow these steps:

### Step 1: Rewrite the expression
We start with the expression:
\[ \sqrt[3]{\frac{-64}{125}} \]
This can be rewritten using the property of cube roots:
\[ \sqrt[3]{\frac{-64}{125}} = \frac{\sqrt[3]{-64}}{\sqrt[3]{125}} \]

### Step 2: Evaluate the cube root of the numerator
Next, we evaluate the cube root of \(-64\):
\[ \sqrt[3]{-64} = -4 \]
This is because \((-4) \times (-4) \times (-4) = -64\).

### Step 3: Evaluate the cube root of the denominator
Now, we evaluate the cube root of \(125\):
\[ \sqrt[3]{125} = 5 \]
This is because \(5 \times 5 \times 5 = 125\).

### Step 4: Combine the results
Now we can combine the results from steps 2 and 3:
\[ \frac{\sqrt[3]{-64}}{\sqrt[3]{125}} = \frac{-4}{5} \]

### Final Answer
Thus, the final result is:
\[ \sqrt[3]{\frac{-64}{125}} = -\frac{4}{5} \]

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