Answer
$4x^{3}$
Work Step by Step
Multiplying the numerators and the denominators, the given expression, $ \dfrac{x^2y}{4}\cdot\dfrac{16x}{y} ,$ is equivalent to \begin{align*} \dfrac{x^2y(16x)}{4y} .\end{align*} Using the laws of exponents, the expression above is equivalent to \begin{align*}\require{cancel} & \dfrac{16x^{2+1}y}{4y}
\\\\&=
\dfrac{16x^{3}y}{4y}
\\\\&=
\dfrac{4x^{3}\cdot4y}{4y}
\\\\&=
\dfrac{4x^{3}\cdot\cancel{4y}}{\cancel{4y}}
\\\\&=
4x^{3}
.\end{align*} Hence, the simplified form of the given expression is $
4x^{3}
$.
