\( 10 p^{3}+-11 p^{7} q+6 q+4 \) Simpliy \( \left(\frac{2}{3} x^{3}-\frac{1}{y^{2}}\right)\left(\frac{1}{2} x^{2}-\frac{4}{3} x y-\frac{1}{2} y^{2}\right)(y \neq 0 \)

Let's simplify the polynomial \( 10 p^{3} - 11 p^{7} q + 6 q + 4 \). We can rearrange it into standard form: \( -11 p^{7} q + 10 p^{3} + 6 q + 4 \). Since the terms can't be combined, this is the simplest expression in this form. For the product \( \left(\frac{2}{3} x^{3}-\frac{1}{y^{2}}\right)\left(\frac{1}{2} x^{2}-\frac{4}{3} x y-\frac{1}{2} y^{2}\right) \), we can use the distributive property (FOIL method) to multiply both polynomials. This will result in multiple terms, which are then simplified by combining like terms. The result is a cubic polynomial in \( x \) and \( y \) successfully expressed in one equation.