2x^-7*3x^5/6x^-2

To simplify the expression \( \frac{2x^{-7} \cdot 3x^{5}}{6x^{-2}} \), follow these steps:

1. Multiply the coefficients and combine the powers of \( x \) in the numerator: \[ 2 \cdot 3 = 6 \quad \text{and} \quad x^{-7} \cdot x^{5} = x^{-2} \quad \text{(since } -7 + 5 = -2\text{)} \] Thus, the numerator becomes: \[ 6x^{-2} \]

2. Now substituting back into the expression we get: \[ \frac{6x^{-2}}{6x^{-2}} \]

3. Since \( \frac{6}{6} = 1 \), and \( x^{-2} \) cancels out: \[ 1 \]

Thus, the simplified expression is: \[ \boxed{1} \]