Find the cube - roots of :
`700xx2xx49xx5`

Answer

To find the cube root of the expression \( 700 \times 2 \times 49 \times 5 \), we will follow these steps:

### Step 1: Factorize each number
First, we will factorize each number in the expression.

- **700** can be factorized as:
\[ 700 = 7 \times 100 = 7 \times (10 \times 10) = 7 \times (2 \times 5) \times (2 \times 5) = 7 \times 2^2 \times 5^2 \]

- **49** can be factorized as:
\[ 49 = 7 \times 7 = 7^2 \]

- **2** is already a prime number, so it remains as \( 2^1 \).

- **5** is also a prime number, so it remains as \( 5^1 \).

### Step 2: Combine the factors
Now we can combine all the factors together:
\[ 700 \times 2 \times 49 \times 5 = (7 \times 2^2 \times 5^2) \times (2^1) \times (7^2) \times (5^1) \]

### Step 3: Group the factors
Now we will group the same bases together:
\[ = 7^{1+2} \times 2^{2+1} \times 5^{2+1} = 7^3 \times 2^3 \times 5^3 \]

### Step 4: Write the expression under the cube root
Now we can write the entire expression under the cube root:
\[ \sqrt[3]{7^3 \times 2^3 \times 5^3} \]

### Step 5: Simplify the cube root
Using the property of cube roots, we can take out the bases:
\[ = \sqrt[3]{7^3} \times \sqrt[3]{2^3} \times \sqrt[3]{5^3} = 7 \times 2 \times 5 \]

### Step 6: Calculate the final result
Now we can calculate the final result:
\[ = 7 \times 2 = 14 \]
\[ 14 \times 5 = 70 \]

Thus, the cube root of \( 700 \times 2 \times 49 \times 5 \) is \( 70 \).

### Final Answer:
The cube root is \( 70 \).

---