Answer
$\frac{6}{25}$
Work Step by Step
$\frac{15\times4xy\times9}{6\times25x\times15y}\longrightarrow$ Use prime factorization.
$\frac{3\times5\times2\times2\times xy\times3\times3}{2\times3\times5\times5\times x\times3\times5\times y}\longrightarrow$ Reorder
$\frac{2\times2\times3\times3\times3\times5\times x\times y}{2\times3\times3\times5\times5\times5\times x\times y}\longrightarrow$ Identify factors that cancel (indicated with line over the top).
$\frac{\overline{2}\times2\times\overline{3}\times\overline{3}\times3\times\overline{5}\times \overline{x}\times \overline{y}}{\overline{2}\times\overline{3}\times\overline{3}\times\overline{5}\times5\times5\times \overline{x}\times \overline{y}}\longrightarrow$ Eliminate canceled factors.
$\frac{2\times3}{5\times5}$ Simplify.
$\frac{6}{25}$
