The complex number can be written as,

\(\displaystyle{\left(\sqrt{{3}}-{i}\right)}={2}{\left(\frac{\sqrt{{3}}}{{2}}-{i}\frac{{1}}{{2}}\right)}\)

\(\displaystyle{\left(\sqrt{{3}}-{i}\right)}={2}{\left({\cos{{\left(-\frac{\pi}{{6}}\right)}}}+{i}{\sin{{\left(-\frac{\pi}{{6}}\right)}}}\right)}\)

therefore, it can be represented as,

\(\displaystyle{2}{\left({\cos{{\left(-\frac{\pi}{{6}}\right)}}}+{i}{\sin{{\left(-\frac{\pi}{{6}}\right)}}}\right)}={2}{e}^{{-{i}{\left(\frac{\pi}{{6}}\right)}}}\)

therefore,

\(\displaystyle{\left(\sqrt{{3}}-{i}\right)}^{{6}}={\left[{2}{e}^{{-{i}{\left(\frac{\pi}{{6}}\right)}}}\right]}^{{6}}={2}^{{6}}{e}^{{-{i}\pi}}={64}{e}^{{-\pi}}\)

Therefore ,the given complex number can be simplified further as,

\(\displaystyle{\left(\sqrt{{3}}-{i}\right)}^{{6}}={64}{\left({\cos{{\left(-\pi\right)}}}+{i}{\sin{{\left(-\pi\right)}}}\right)}={64}\cdot{\left(-{1}\right)}+{i}{0}{)}={64}\cdot{\left(-{1}\right)}=-{64}\)

Hence, the given complex number becomes −64.

\(\displaystyle{\left(\sqrt{{3}}-{i}\right)}={2}{\left(\frac{\sqrt{{3}}}{{2}}-{i}\frac{{1}}{{2}}\right)}\)

\(\displaystyle{\left(\sqrt{{3}}-{i}\right)}={2}{\left({\cos{{\left(-\frac{\pi}{{6}}\right)}}}+{i}{\sin{{\left(-\frac{\pi}{{6}}\right)}}}\right)}\)

therefore, it can be represented as,

\(\displaystyle{2}{\left({\cos{{\left(-\frac{\pi}{{6}}\right)}}}+{i}{\sin{{\left(-\frac{\pi}{{6}}\right)}}}\right)}={2}{e}^{{-{i}{\left(\frac{\pi}{{6}}\right)}}}\)

therefore,

\(\displaystyle{\left(\sqrt{{3}}-{i}\right)}^{{6}}={\left[{2}{e}^{{-{i}{\left(\frac{\pi}{{6}}\right)}}}\right]}^{{6}}={2}^{{6}}{e}^{{-{i}\pi}}={64}{e}^{{-\pi}}\)

Therefore ,the given complex number can be simplified further as,

\(\displaystyle{\left(\sqrt{{3}}-{i}\right)}^{{6}}={64}{\left({\cos{{\left(-\pi\right)}}}+{i}{\sin{{\left(-\pi\right)}}}\right)}={64}\cdot{\left(-{1}\right)}+{i}{0}{)}={64}\cdot{\left(-{1}\right)}=-{64}\)

Hence, the given complex number becomes −64.