Simplify: y. \( \frac{\left(x^{4} y\right)^{3} \times\left(9 x y^{2}\right)^{2}}{(2 y)^{0} \times\left(3 x^{2}\right)^{3}} \)

To simplify the expression \( \frac{\left(x^{4} y\right)^{3} \times\left(9 x y^{2}\right)^{2}}{(2 y)^{0} \times\left(3 x^{2}\right)^{3}} \), we begin by applying the exponent rules. 1. **Numerator**: - \((x^{4} y)^{3} = x^{12} y^{3}\) - \((9 x y^{2})^{2} = 81 x^{2} y^{4}\) Combining these gives: \[ x^{12} y^{3} \times 81 x^{2} y^{4} = 81 x^{14} y^{7} \] 2. **Denominator**: - \((2 y)^{0} = 1\) - \((3 x^{2})^{3} = 27 x^{6}\) Thus, the denominator simplifies to: \[ 1 \times 27 x^{6} = 27 x^{6} \] Now, we can rewrite the entire expression as: \[ \frac{81 x^{14} y^{7}}{27 x^{6}} \] Next, we divide the coefficients (81 by 27) and apply the quotient rule for the variable \(x\): \[ = 3 x^{14-6} y^{7} = 3 x^{8} y^{7} \] So, the simplified expression is: \[ \boxed{3 x^{8} y^{7}} \]