Answer:
[tex]\frac{x^{3} }{9y^{4} }[/tex]
Step-by-step explanation:
The given expression is
[tex]\frac{(xy)^{-2} }{(3y)^{2} x^{-5} }[/tex]
First, we use the property: [tex](xy)^{2} =x^{2} y^{2}[/tex]
[tex]\frac{(xy)^{-2} }{(3y)^{2} x^{-5} }=\frac{x^{-2} y^{-2} }{9y^{2} x^{-5} }[/tex]
Then, we use the property: [tex]\frac{x^{m} }{x^{n} }=x^{m-n}[/tex]
[tex]\frac{x^{-2} y^{-2} }{9y^{2} x^{-5} }=\frac{x^{-2+5} y^{-2-2} }{9} =\frac{x^{3}y^{-4} }{9}[/tex]
Next, we use the property: [tex]x^{-n} =\frac{1}{x^{-n} }[/tex]
[tex]\frac{x^{3}y^{-4} }{9}=\frac{x^{3} }{9y^{4} }[/tex]
Therefore, the answer is
[tex]\frac{x^{3} }{9y^{4} }[/tex]
