Question

What is the solution to the equation?−6=x8Enter your answer in the box.

Answer 1

`-6=x^8`

Solve for x:

Take the 8th root of both sides:

`\begin{gathered} \sqrt[8]{-6}=\sqrt[8]{x^8} \\ so\colon \\ x=\sqrt[8]{6(-1)} \\ x=\sqrt[8]{6}\cdot\sqrt[8]{-1} \\ Using_{\text{ }}the_{\text{ }}polar_{\text{ }}form \\ x=-\sqrt[8]{6}\cos ((\pi)/(8))-i\sqrt[8]{6}\sin ((\pi)/(8)) \end{gathered}`