Question

I need help with this problem Evaluate each expression given the variable replacement

Answer 1

Given the expression:

`(20ab)/(\mleft(a-b\mright)^2)`

1. You need to substitute these values given in the exercise into the expression:

`\begin{gathered} a=4 \\ b=-2 \end{gathered}`

Then:

`=(20(4)(-2))/((4-(-2))^2)`

2. According to the Sign Rules for Multiplication:

`\begin{gathered} +\cdot+=+ \\ -\cdot-=+ \\ -\cdot+=- \\ +\cdot-=- \end{gathered}`

Knowing this, you can solve the multiplication in the numerator and simplify the denominator:

`=(-160)/((4+2)^2)`
`=(-160)/((6)^2)`

You know that:

`6^2=6\cdot6=36`

Then:

`=(-160)/(36)`

3. According to the Sign Rules for Division:

`\begin{gathered} (-)/(-)=+ \\ \\ (+)/(+)=+ \\ \\ (-)/(+)=- \\ \\ (+)/(-)=- \end{gathered}`

Therefore, since the numerator is negative and the denominator is positive, the fraction is negative:

`=-(160)/(36)`

4. You can reduce the fraction by dividing the numerator and the denominator by 4:

`\begin{gathered} =-(160/4)/(36/4) \\ \\ =-(40)/(9) \end{gathered}`

Hence, the answer is:

`=-(40)/(9)`