Answer
$40,320$
Work Step by Step
The given expression, $
8\cdot7\cdot6\cdot5\cdot4\cdot3\cdot2\cdot1
,$ simplifies to
\begin{array}{l}\require{cancel}
56\cdot6\cdot5\cdot4\cdot3\cdot2\cdot1
\\\\=
336\cdot5\cdot4\cdot3\cdot2\cdot1
\\\\=
1,680\cdot4\cdot3\cdot2\cdot1
\\\\=
6,720\cdot3\cdot2\cdot1
\\\\=
20,160\cdot2\cdot1
\\\\=
40,320\cdot1
\\\\=
40,320
.\end{array}