find the number of digits in the number 2 to the power 2005 into 5 to the power 2000
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2^2005 x 5^2000=
2^2000 x 5^2000 x 2^5=
(2x5)^2000 x 32
10^2000 x 32
one followed by 2000 zeroes into 32
therefore 2002 digits cause 10 to the power of anything will add the zeroes as digit.
for ex:
10x32=320
ie 3 digits
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