Problem: What is the sum of the digits of the decimal form of the product 21999⋅52001?2^{1999} \cdot 5^{2001}?21999⋅52001?
Answer Choices:
A. 222
B. 444
C. 555
D. 777
E. 101010
Solution:
Note that
21999⋅52001=21999⋅51999⋅52=101999⋅25=250…0⏞1999 2eros .2^{1999} \cdot 5^{2001}=2^{1999} \cdot 5^{1999} \cdot 5^{2}=10^{1999} \cdot 25=25 \overbrace{0 \ldots 0}^{1999 \text { 2eros }} . 21999⋅52001=21999⋅51999⋅52=101999⋅25=250…01999 2eros .
Hence the sum of the digits is 777.