Answer
$-\dfrac{27}{2} -\dfrac{2 7\sqrt3}{2}i$
Work Step by Step
De Moivre's Theorem states that $(\cos{x}+i\sin{x})^a=\cos{(ax)}+\ i \sin{(ax)}$
Apply the theorem above to obtain:
$\left[3(\cos 80^\circ+i\sin 80^\circ\right]^3
\\=3^3\left[\cos(3\cdot 80^\circ)+i \sin(3\cdot 80^\circ)\right]
\\=27\left[\cos240^\circ+i\sin{240^\circ}\right]
\\=27\left[-\frac{1}{2}+i\cdot \left(\frac{-\sqrt3}{2}\right)\right]
\\=-\dfrac{27}{2} -\dfrac{2 7\sqrt3}{2}i$
