Solve for: (4y^3) * ((3)/(4)xy^4) * (-3x^2y^2)

Expression: $\left( 4{y}^{3} \right) \times \left( \frac{ 3 }{ 4 }x{y}^{4} \right) \times \left( -3{x}^{2}{y}^{2} \right)$

Multiplying a positive and a negative equals a negative: $\left( + \right) \times \left( - \right)=\left( - \right)$

$-4{y}^{3} \times \frac{ 3 }{ 4 }x{y}^{4} \times 3{x}^{2}{y}^{2}$

Cancel out the greatest common factor $4$

$-{y}^{3} \times 3x{y}^{4} \times 3{x}^{2}{y}^{2}$

Calculate the product

$-9{x}^{3}{y}^{9}$