Question

Simplify the expression.6 -6 3X yx-9y-3Write your answer without negative exponents.Enter the correct answer.

Answer 1

The given expression is:

`\left((x^(-6)y^(-6))/(x^(-9)y^(-3))\right)^{(1)/(3)}`

Apply the Quotient of Powers Property to the expression:

`\begin{gathered} \left(x^(-6-(-9))y^(-6-(-3))\right)^{(1)/(3)} \\ =(x^(-6+9)y^(-6+3))^{(1)/(3)}=(x^3y^(-3))^{(1)/(3)} \end{gathered}`

Using the Power of Product Property, it follows:

`\begin{gathered} =(x^3)^{(1)/(3)}(y^(-3))^{(1)/(3)} \\ =x^{3\cdot(1)/(3)}y^{-3\cdot(1)/(3)}=x^1\cdot y^(-1)=(x)/(y) \end{gathered}`

The answer is x/y.