Simplify : `343xx2^(3)div(14)^3`

Answer

To simplify the expression \( \frac{343 \times 2^3}{14^3} \), we can follow these steps:

### Step 1: Rewrite 343 as a power of its prime factors
We know that \( 343 = 7 \times 7 \times 7 = 7^3 \).

### Step 2: Rewrite the expression
Now we can rewrite the expression:
\[ \frac{343 \times 2^3}{14^3} = \frac{7^3 \times 2^3}{14^3} \]

### Step 3: Rewrite 14 as a product of its prime factors
Next, we can express \( 14 \) in terms of its prime factors:
\[ 14 = 2 \times 7 \]
Thus, \( 14^3 = (2 \times 7)^3 = 2^3 \times 7^3 \).

### Step 4: Substitute back into the expression
Now we can substitute \( 14^3 \) back into the expression:
\[ \frac{7^3 \times 2^3}{2^3 \times 7^3} \]

### Step 5: Simplify the expression
Now, we can simplify the expression by canceling out the common terms in the numerator and denominator:
\[ \frac{7^3 \times 2^3}{2^3 \times 7^3} = 1 \]

### Final Answer
Thus, the simplified value of the expression \( \frac{343 \times 2^3}{14^3} \) is:
\[ \boxed{1} \]