Question

Simplify. Do not leave negative exponents in your answer.

(x^9/(-27y^3))^(-2/3)

Answer 1

\[(x^9/-27y^3)^-2/3\]

Answer 2

\[\left( \frac{x^9}{-27y^3} \right)^{-2/3}\]Recall that \[\large {x^{\frac ab}=\sqrt[b]{x^a}}\]and \[\large x^{-a}=\frac{1}{x^a}\]

Answer 3

\[\left( \frac{x^9}{-27y^3} \right)^{-2/3}=\sqrt[3]{\left( \frac{x^9}{-27y^3} \right)^{-2}}=\sqrt[3]{\left( \frac{-27y^3}{x^9} \right)^2}\]

Answer 4

I'm not completely sure about the negative sign.

Answer 5

Without the negative sign, I think this would simplify down to \[\pm \frac{9y^2}{x^6}\]

Answer 6

Maybe\[\pm \frac{9y^2}{x^6}i\]

Answer 7

Thank you

Answer 8

= [ ( - 3³ y³ )/ x^9 ]^ (2/3)
= ( -3y/x³ )²
= 9y²/ x^6