Answer
$\dfrac{1}{2.7^{\frac{3}{4}}}$
Work Step by Step
Using the laws of exponents, the given expression, $
\dfrac{2.7^{-11/12}}{2.7^{-1/6}}
,$ simplifies to
\begin{array}{l}\require{cancel}
2.7^{-\frac{11}{12}-\left( -\frac{1}{6} \right)}
\\\\=
2.7^{-\frac{11}{12}+\frac{1}{6}}
\\\\=
2.7^{-\frac{11}{12}+\frac{2}{12}}
\\\\=
2.7^{-\frac{9}{12}}
\\\\=
2.7^{-\frac{3}{4}}
\\\\=
\dfrac{1}{2.7^{\frac{3}{4}}}
.\end{array}
