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

`((xy)^(-2))/((3y)^2x^(-5))=(x^(-2)y^(-2))/(9y^2x^(-5))=(x^3)/(9y^4)`

Answer 2

`(x^(3) )/(9y^(4) )`

Explanation:

The given expression is

`((xy)^(-2) )/((3y)^(2) x^(-5) )`

First, we use the property:
`(xy)^(2) =x^(2) y^(2)`

`((xy)^(-2) )/((3y)^(2) x^(-5) )=(x^(-2) y^(-2) )/(9y^(2) x^(-5) )`

Then, we use the property:
`(x^(m) )/(x^(n) )=x^(m-n)`

`(x^(-2) y^(-2) )/(9y^(2) x^(-5) )=(x^(-2+5) y^(-2-2) )/(9) =(x^(3)y^(-4) )/(9)`

Next, we use the property:
`x^(-n) =(1)/(x^(-n) )`

`(x^(3)y^(-4) )/(9)=(x^(3) )/(9y^(4) )`

Therefore, the answer is

`(x^(3) )/(9y^(4) )`