05AB1E, 5 4 bytes
$g×*
-1 byte porting emanresuA's Jelly answer
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Original 5 bytes answer: Alternative 4-byter (port of @Bubbler's Japt answer:
ā<°*OgиTβ
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Explanation:
$ # Push 1 and the input
g # Pop the input, and push its length
× # Repeat 1 that many times
* # Multiply it to the (implicit) input-integer
# (after which the result is output implicitly)
ā g # Push athe listlength inof the range [1, (implicit) input-length] (without popping)integer
< и # Decrease it toRepeat the range [0, length(implicit)
° # Get 10 to the power each valueinput-list inthat themany listtimes
* Tβ # Multiply each by the input that's still on the stack
Convert it from a Obase-10 list #to Suma itbase-10 togetherinteger
# (after which the result is output implicitly)