Question 119127
*[Tex \LARGE \sqrt[3]{-27n^{27}}] Start with the given expression



*[Tex \LARGE \left(-27n^{27}\right)^{\frac{1}{3}}] Convert the expression from radical notation to exponent notation. Remember *[Tex \LARGE \sqrt[3]{A}=A^{\frac{1}{3}}]



 *[Tex \LARGE \left((-27)^1n^27\right)^{\frac{1}{3}}] Rewrite -27 as {{{-27^1}}}



 *[Tex \LARGE (-27)^{1\left(\frac{1}{3}\right)}n^{27\left(\frac{1}{3}\right)}] Now distribute the exponent Now distribute the outer exponent {{{1/3}}} to each exponent in the parenthesis. Remember {{{(x^y)^z=x^(y*z)}}}


 

 *[Tex \LARGE (-27)^{\frac{1}{3}}n^{\frac{27}{3}}] Now multiply the exponents


 

 *[Tex \LARGE (-27)^{\frac{1}{3}}n^{9}] Reduce




 *[Tex \LARGE \sqrt[3]{-27}n^{9}] Now rewrite *[Tex \LARGE (-27)^{\frac{1}{3}}] as *[Tex \LARGE \sqrt[3]{-27}]



*[Tex \LARGE -3n^{9}] Take the cube root of -27 to get -3




So *[Tex \LARGE \sqrt[3]{-27n^{27}}] simplifies to *[Tex \LARGE -3n^{9}]