How many digits does the number 1000^1000 have?

Question

Suppose 4 digits 2 ,4,6 and 9 are given.
You have to make a four-digit number.
In how many ways it can be done, if repetition of the numbers does not allowed?

Answer 1

Number of Zeros in the result : 3 * 1000 or 3000
Total Digits: 3001 (including 1)

Answer 2

i think explanation should be given as under
(1000)^1000=(10^3)^1000=10^(3*1000)=10^3000
since 10^n has n zeros, the number of zeros are 3000 therefore including one digits are 3000

Answer 3

Ans is 'Infinity'