(8) \( \frac{-(3 x)^{2} \cdot(-2 x)^{3}}{\left(-3 \times 2 x^{2}\right)^{2}} \)

To simplify the expression \( \frac{-(3 x)^{2} \cdot(-2 x)^{3}}{\left(-3 \times 2 x^{2}\right)^{2}} \), let's break it down step by step. First, simplify the numerator: 1. \( (3x)^2 = 9x^2 \) 2. \( (-2x)^3 = -8x^3 \) Now, combine these: \[ -(3x)^{2} \cdot (-2x)^{3} = - (9x^2) \cdot (-8x^3) = 9x^2 \cdot 8x^3 = 72x^{5} \] Now, simplify the denominator: 1. \( (-3 \times 2x^2) = -6x^2 \) 2. When squaring this: \[ (-6x^2)^2 = 36x^4 \] Now we can put it all together: \[ \frac{72x^{5}}{36x^{4}} = \frac{72}{36} \cdot \frac{x^{5}}{x^{4}} = 2 \cdot x^{1} = 2x \] Thus, the simplified form of the expression is: \[ \boxed{2x} \]