Question

Simplify the following expression using the properties of exponents. The final form of the expressionswith variables should contain only positive exponents. Assume that all variables represent nonzeronumbers.- &x y-22x3y3AnswerKeypadKeyboard Shortcuts

Answer 1

The given expression is,

`(-8x^5y^(-2))/(2x^3y^3)`

Factor out the number:

`\begin{gathered} 8=2\cdot\: 4 \\ =(-2\cdot\:4x^5y^(-2))/(2x^3y^3) \end{gathered}`

Cancel out the common factor: 2

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

Simplify the above

`(x^5)/(x^3)=x^2`

Therefore,

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

Simplify

`(y^(-2))/(y^3)=(1)/(y^5)`
`=(-4x^2)/(y^5)`

Apply the fraction rule

`(-a)/(b)=-(a)/(b)`
`=-(4x^2)/(y^5)`

Hence, the answer is

`-(4x^2)/(y^5)`