Question

Divide (7x^5y-14x^5y^5) divided by (-2x^2y^4)Simplify your answer as much as possible

Answer 1

We need to simplify the expression:

`(7x^5y-14x^5y^5)/(-2x^2y^4)`

We can start by writting:

`\begin{gathered} (7x^5y-14x^5y^5)/(-2x^2y^4)=\frac{7x^5y(1-2y^4)^{}}{-2x^2y^4} \\ \\ =-(7)/(2)\cdot(x^5)/(x^2)\cdot(y)/(y^4)\cdot(1-2y^4)^{} \end{gathered}`

Now, we can use the rule:

`(z^a)/(z^b)=z^(a-b)`

We obtain:

`\begin{gathered} -(7)/(2)x^(5-2)y^(1-4)(1-2y^4) \\ \\ -(7)/(2)x^3y^(-3)(1-2y^4) \\ \\ (7)/(2)x^3y^(-3)(2y^4-1) \\ \\ (7x^3\mleft(2y^4-1\mright))/(2y^(3)) \end{gathered}`

Therefore, after simplifying, we obtain:

`(7x^3(2y^4-1))/(2y^3)`