Combinatorial products of unique primes
Pure Bash, 32 bytes
eval echo \$[{1,${1// /\}*{1,}}]

Reads input list (single space separated) passed as a command-line arg.
Three different shell expansions are used:

${1// /\}*{1,} is a parameter expansion that replaces spaces in 2 3 5 7 with }*{1, to give 2}*{1,3}*{1,5}*{1,7.  \$[{1, and }] are added to the start and end respectively to give \$[{1,2}*{1,3}*{1,5}*{1,7}].  The \$[ is backslash-escaped to prevent attempts to do arithmetic expansion at this stage.
\$[{1,2}*{1,3}*{1,5}*{1,7}] is a brace expansion.  Because brace expansion typically happens before parameter expansion, we use have to useeval to force the parameter expansion to happen first.  The result of the brace expansion is $[1*1*1*1] $[1*1*1*7] $[1*1*5*1] ... $[2*3*5*7].
$[1*1*1*1] $[1*1*1*7] $[1*1*5*1] ... $[2*3*5*7] is a list of arithmetic expansions, which are then evaluated to give the list of numbers we require.

Output:
$ ./comboprime.sh &quot;2 3 5 7&quot;
1 7 5 35 3 21 15 105 2 14 10 70 6 42 30 210
$