Answer
$4\sqrt{3}+4i$.
Work Step by Step
Here
$\begin{align}
& z={{\left[ 2\left( \cos {{10}^{{}^\circ }}+i\sin {{10}^{{}^\circ }} \right) \right]}^{3}} \\
& z={{2}^{3}}\left( \cos 3\times {{10}^{{}^\circ }}+i\sin 3\times {{10}^{{}^\circ }} \right) \\
& z=8\left( \cos {{30}^{{}^\circ }}+i\sin {{30}^{{}^\circ }} \right) \\
& z=8\left( \frac{\sqrt{3}}{2}+i\frac{1}{2} \right) \\
\end{align}$
Simplifying it further, to get,
$z=4\sqrt{3}+4i$
The power of the complex number in the rectangular form is $4\sqrt{3}+4i$
