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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

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/(x class=

Verified Answer :

konrad509

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

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

\(\frac{x^{3} }{9y^{4} }\)

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