Evaluate: ((2yx^{-3})^3)/(x^0y^2 * 2x^3y^3)

Expression: $\frac{ {\left( 2y{x}^{-3} \right)}^{3} }{ {x}^{0}{y}^{2} \times 2{x}^{3}{y}^{3} }$

To raise a product to a power, raise each factor to that power

$\frac{ 8{y}^{3}{x}^{-9} }{ {x}^{0}{y}^{2} \times 2{x}^{3}{y}^{3} }$

Any non-zero expression raised to the power of $0$ equals $1$

$\frac{ 8{y}^{3}{x}^{-9} }{ 1{y}^{2} \times 2{x}^{3}{y}^{3} }$

Any expression multiplied by $1$ remains the same

$\frac{ 8{y}^{3}{x}^{-9} }{ {y}^{2} \times 2{x}^{3}{y}^{3} }$

Cancel out the common factor ${y}^{3}$

$\frac{ 8{x}^{-9} }{ {y}^{2} \times 2{x}^{3} }$

Cancel out the common factor $2$

$\frac{ 4{x}^{-9} }{ {y}^{2}{x}^{3} }$

Simplify the expression

$\frac{ 4 }{ {y}^{2}{x}^{12} }$

Use the commutative property to reorder the terms

$\frac{ 4 }{ {x}^{12}{y}^{2} }$