Answer
$\dfrac{7}{9w^{6}}$
Work Step by Step
Using the laws of exponents, the given expression, $
\dfrac{7w^8}{9w^{14}}
,$ simplifies to
\begin{array}{l}\require{cancel}
\dfrac{7w^{8-14}}{9}
\\\\=
\dfrac{7w^{-6}}{9}
\\\\=
\dfrac{7}{9w^{6}}
.\end{array}