Evaluate: (x^{-4}z^5) * ((2x^3y)/(z^{-1)})^{-3}

Expression: $\left( {x}^{-4}{z}^{5} \right) \times {\left( \frac{ 2{x}^{3}y }{ {z}^{-1} } \right)}^{-3}$

Remove unnecessary parentheses

${x}^{-4}{z}^{5} \times {\left( \frac{ 2{x}^{3}y }{ {z}^{-1} } \right)}^{-3}$

Express with a positive exponent using ${\left( \frac{ a }{ b } \right)}^{-n}={\left( \frac{ b }{ a } \right)}^{n}$

${x}^{-4}{z}^{5} \times {\left( \frac{ {z}^{-1} }{ 2{x}^{3}y } \right)}^{3}$

To raise a fraction to a power, raise the numerator and denominator to that power

${x}^{-4}{z}^{5} \times \frac{ {z}^{-3} }{ 8{x}^{9}{y}^{3} }$

Cancel out the common factor ${x}^{-4}$

${z}^{5} \times \frac{ {z}^{-3} }{ 8{x}^{13}{y}^{3} }$

Calculate the product

$\frac{ {z}^{2} }{ 8{x}^{13}{y}^{3} }$