Answer
$\frac{5ap}{2cm}$
Work Step by Step
$\frac{\frac{27ab}{15mn}}{\frac{18bc}{25np}}\longrightarrow$ Divide fractions by multiplying the inverse of the denominator.
$\frac{27ab}{15mn}\times\frac{25np}{18bc}\longrightarrow$ Use prime factorization.
$\frac{3\times3\times3\times a\times b}{3\times5\times m\times n}\times\frac{5\times5\times n\times p}{2\times3\times3\times b\times c}\longrightarrow$ Identify factors that cancel (marked with a line over the top).
$\frac{\overline{3}\times\overline{3}\times\overline{3}\times a\times \overline{b}}{\overline{3}\times\overline{5}\times m\times \overline{n}}\times
\frac{\overline{5}\times5\times \overline{n}\times p}
{2\times\overline{3}\times\overline{3}\times \overline{b}\times c}\longrightarrow$ Eliminate canceled factors.
$\frac{5ap}{2cm}$
