Question

uestion 4 of 10structions: Select the correct answer from the drop down menu.(xy)nsider the expressione equivalent simplified form of this expression isx 3/9/(xn-7)ext Reset

Answer 1

$\dfrac{(xy)^{-2}}{(3y)^2x^{-5}}=\dfrac{x^{-2}y^{-2}}{9y^2x^{-5}}=\dfrac{x^3}{9y^4}$

Answer 2

Answer:

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

Step-by-step explanation:

The given expression is

$\frac{(xy)^{-2} }{(3y)^{2} x^{-5} }$

First, we use the property: $(xy)^{2} =x^{2} y^{2}$

$\frac{(xy)^{-2} }{(3y)^{2} x^{-5} }=\frac{x^{-2} y^{-2} }{9y^{2} x^{-5} }$

Then, we use the property: $\frac{x^{m} }{x^{n} }=x^{m-n}$

$\frac{x^{-2} y^{-2} }{9y^{2} x^{-5} }=\frac{x^{-2+5} y^{-2-2} }{9} =\frac{x^{3}y^{-4} }{9}$

Next, we use the property: $x^{-n} =\frac{1}{x^{-n} }$

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

Therefore, the answer is

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