Find the cube-roots of :
`-125xx1000`

Answer

To find the cube root of the expression \(-125 \times 1000\), we can follow these steps:

### Step 1: Factor the numbers
First, we need to factor both \(-125\) and \(1000\).

- The number \(-125\) can be factored as:
\[ -125 = -1 \times 125 = -1 \times 5^3 \]

- The number \(1000\) can be factored as:
\[ 1000 = 10^3 \]

### Step 2: Combine the factors
Now, we can combine these factors:
\[ -125 \times 1000 = (-1 \times 5^3) \times (10^3) \]
This can be simplified to:
\[ = -1 \times (5 \times 10)^3 \]

### Step 3: Simplify the expression
Now, we can simplify \(5 \times 10\):
\[ 5 \times 10 = 50 \]
Thus, we can rewrite the expression as:
\[ -1 \times 50^3 \]

### Step 4: Find the cube root
Now, we can find the cube root of the entire expression:
\[ \sqrt[3]{-1 \times 50^3} = \sqrt[3]{-1} \times \sqrt[3]{50^3} \]
We know that:
\[ \sqrt[3]{-1} = -1 \quad \text{and} \quad \sqrt[3]{50^3} = 50 \]
So, we have:
\[ \sqrt[3]{-125 \times 1000} = -1 \times 50 = -50 \]

### Final Answer
The cube root of \(-125 \times 1000\) is:
\[ \boxed{-50} \]

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