Answer
$\dfrac{2x^{6}}{5}$
Work Step by Step
Using the laws of exponents, the given expression, $
\dfrac{2x^5\cdot3x^7}{15x^6}
,$ simplifies to
\begin{array}{l}\require{cancel}
\dfrac{2(3)x^{5+7-6}}{15}
\\\\=
\dfrac{2(\cancel{3})x^{5+7-6}}{\cancel{3}(5)}
\\\\=
\dfrac{2x^{6}}{5}
.\end{array}