Indices Question with negative numerator

$27^{-\frac{1}{2}} \\~\\ =\,\frac1{27^{\frac12}} \\~\\ =\,\frac1{\sqrt{27}} \\~\\ =\,\frac{1}{\sqrt{3*3*3}} \\~\\ =\,\frac1{3\sqrt3} \\~\\ =\,\frac{\sqrt3}{9}$