Which shows how to find the value of this expression when x-2 and y=5(3 {x}^(3) {y}^{ - 2)2

Question

which shows how to find the value of this expression when x-2 and y=5
`(3 {x}^(3) {y}^{ - 2)2`

Answer 1

Here we have the expression:

`(3x^3y^(-2))^2`

We want to find its value when x = -2 and y = 5. For this, we could replace the value of each variable:

`(3\cdot(-2)^3(5)^(-2))^2`

Remember that:

`\begin{gathered} (-2)^3=(-2)(-2)(-2)=-8 \\ \\ (5)^(-2)=(1)/(5^2)=(1)/(25) \end{gathered}`

Replacing these values:

`(3\cdot(-8)((1)/(25)))^2=(-(24)/(25))^2=(576)/(625)=0.9216`

Which is the same that:

`(3^2(-2)^6)/(5^4)`

So the correct option is A.