The given expression is:
[tex]\left(\frac{x^{-6}y^{-6}}{x^{-9}y^{-3}}\right)^{\frac{1}{3}}[/tex]
Apply the Quotient of Powers Property to the expression:
[tex]\begin{gathered} \left(x^{-6-(-9)}y^{-6-(-3)}\right)^{\frac{1}{3}} \\ =(x^{-6+9}y^{-6+3})^{\frac{1}{3}}=(x^3y^{-3})^{\frac{1}{3}} \end{gathered}[/tex]
Using the Power of Product Property, it follows:
[tex]\begin{gathered} =(x^3)^{\frac{1}{3}}(y^{-3})^{\frac{1}{3}} \\ =x^{3\cdot\frac{1}{3}}y^{-3\cdot\frac{1}{3}}=x^1\cdot y^{-1}=\frac{x}{y} \end{gathered}[/tex]
The answer is x/y.
