Question 197974
*[Tex \LARGE \left(-27x^{9}\right)^{\frac{1}{3}}] ... Start with the given expression.



*[Tex \LARGE \sqrt[3]{-27x^{9}}] ... Convert to radical notation.



*[Tex \LARGE \sqrt[3]{-27}\ast \sqrt[3]{x^{9}}] ... Break up the root using the identity {{{root(n,x*y)=root(n,x)*root(n,y)}}}



*[Tex \LARGE \sqrt[3]{(-3)^{3}}\ast \sqrt[3]{x^{9}}] ... Rewrite -27 as {{{(-3)^3}}}



*[Tex \LARGE \sqrt[3]{(-3)^{3}}\ast \sqrt[3]{(x^3)^3}]... Rewrite {{{x^9}}} as {{{(x^3)^3}}}



*[Tex \LARGE -3\ast \sqrt[3]{(x^3)^3}] ... Take the cube root of {{{(-3)^3}}} to get -3



*[Tex \LARGE -3x^3]  ... Take the cube root of {{{(x^3)^3}}} to get {{{x^3}}}




So *[Tex \LARGE \left(-27x^{9}\right)^{\frac{1}{3}} = -3x^3]