Answer
$\dfrac{3x^{7}}{2y^{2}}$
Work Step by Step
Using laws of exponents, then,
\begin{array}{l}
\dfrac{27x^{-5}y^{5}}{18x^{-6}y^{2}}\cdot\dfrac{x^4y^{-2}}{x^{-2}y^3}
\\\\=
\dfrac{3x^{-5-(-6)}y^{5-2}}{2}\cdot x^{4-(-2)}y^{-2-3}
\\\\=
\dfrac{3x^{}y^{3}}{2}\cdot x^{6}y^{-5}
\\\\=
\dfrac{3x^{1+6}y^{3+(-5)}}{2}
\\\\=
\dfrac{3x^{7}y^{-2}}{2}
\\\\=
\dfrac{3x^{7}}{2y^{2}}
.\end{array}
