Answer
$\dfrac{3x^{3}}{4}$
Work Step by Step
Using the laws of exponents, the given expression, $
\dfrac{3x^3\cdot5x^{14}}{20x^{14}}
,$ simplifies to
\begin{array}{l}\require{cancel}
\dfrac{3(5)x^{3+14-14}}{20}
\\\\=
\dfrac{3(\cancel{5})x^{3}}{\cancel{5}(4)}
\\\\=
\dfrac{3x^{3}}{4}
.\end{array}