2. \( \frac{35 x^{7} y^{8}}{7\left(x y^{2}\right)^{3}} \)

To simplify the expression \( \frac{35 x^{7} y^{8}}{7\left(x y^{2}\right)^{3}} \), first simplify the denominator. The term \( \left(x y^{2}\right)^{3} \) can be expanded to \( x^{3} y^{6} \). Thus, the denominator becomes \( 7 x^{3} y^{6} \). Now substituting that back into the expression gives us \( \frac{35 x^{7} y^{8}}{7 x^{3} y^{6}} \). Next, divide the coefficients: \( \frac{35}{7} = 5 \). For the variables \( x \) and \( y \), apply the laws of exponents: \( x^{7}/x^{3} = x^{7-3} = x^{4} \) and \( y^{8}/y^{6} = y^{8-6} = y^{2} \). Putting it all together, the simplified result is \( 5 x^{4} y^{2} \).