Suspected answer:  46^2020

When summing up to various powers of 10, I get the following results:

Sum to       Result

10 ^ 0  =  1
10 ^ 1  =  46
10 ^ 2  =  2116
10 ^ 3  =  97336
10 ^ 4  =  4477456
10 ^ 5  =  205962976
10 ^ 6  =  9474296896

----- code -----

def pod_no_zeros(n):
    """ Input an integer.  Returns the Product of the Digits  """
    aList = list(str(n))
    ans = 1
    for c in aList:
        if int(c) == 0:
            continue
        ans = ans * int(c)
    return ans

for expon in range(7):
    sum_of_pods = 0
    for i in range(1,10**expon+1):
        sum_of_pods += pod_no_zeros(i)
    print(10,'^',expon, '   ', sum_of_pods)