SQL> 
with t(ID,  Period, Val, expected_val) as (select 1, 1, 2, 2
from dual union all select 1, 2, 3, 6
from dual union all select 1, 3, 4, 24
from dual union all select 1, 4, 5, 120
from dual union all select 2, 1, 3, 3
from dual union all select 2, 2, 5, 15
from dual union all select 2, 3, 8, 120
from dual union all select 2, 4, 9, 1080
from dual )
------------------------------------------------
select id, period, val
     , power(10,sum(log(10,val)) over(partition by id order by period)) new_val
from t
;
        ID     PERIOD        VAL    NEW_VAL
---------- ---------- ---------- ----------
         1          1          2          2
         1          2          3          6
         1          3          4         24
         1          4          5        120
         2          1          3          3
         2          2          5         15
         2          3          8        120
         2          4          9       1080
8 rows selected

SQL>