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:

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