Answer
$\dfrac{1}{6}$
Work Step by Step
Using $x^{-a}=\dfrac{1}{x^a}$the given expression, $
3^{-1}-6^{-1}
,$ simplifies to
\begin{array}{l}\require{cancel}
\dfrac{1}{3^1}-\dfrac{1}{6^1}
\\\\=
\dfrac{1}{3}-\dfrac{1}{6}
\\\\=
\dfrac{2}{6}-\dfrac{1}{6}
\\\\=
\dfrac{1}{6}
.\end{array}