${x}^{-4}{z}^{5} \times {\left( \frac{ 2{x}^{3}y }{ {z}^{-1} } \right)}^{-3}$
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$\frac{ {z}^{2} }{ 8{x}^{13}{y}^{3} }$