Step-by-step explanation:
[tex] = {( \frac{3 {x}^{2} y}{x {y}^{ - 1} } )}^{2} \times ( \frac{4 {x}^{ \frac{1}{2}} {y}^{ - 2} }{ \sqrt{27 {x}^{3} } } )[/tex]
[tex] = {(3 {x}^{2 - 1} {y}^{1 - ( - 1)} )}^{2} \times (\frac{4 {x}^{ \frac{1}{2} } {y}^{ - 2} }{ {27}^{ \frac{1}{2} } {x}^{ \frac{3}{2} } } )[/tex]
[tex] = (3x {y}^{2} )^{2} \times ( \frac{4}{ {3}^{ \frac{3}{2} } } {x}^{ \frac{1}{2} - \frac{3}{2} } {y}^{ - 2} )[/tex]
[tex] =( {3}^{2} {x}^{1 \times 2} {y}^{2 \times 2} ) \times ( \frac{4}{ {3}^{ \frac{3}{2} } } {x}^{ - 1} {y}^{ - 2} )[/tex]
[tex] = ( {3}^{2} {x}^{2} {y}^{4} ) \times ( \frac{4}{ {3}^{ \frac{3}{2} } x {y}^{2} } )[/tex]
[tex] =4 \times {3}^{2 - \frac{3}{2} } {x}^{2 - 1} {y}^{4 - 2} [/tex]
[tex] = 4 \times {3}^{ \frac{1}{2} } x {y}^{2} [/tex]
[tex] = 4 \times \sqrt{3} xy[/tex]
[tex] = 4xy \sqrt{3} [/tex]
