Problem: The number of digits in 4165254^{16} 5^{25}416525 (when written in the usual base 101010 form) is
Answer Choices:
A. 313131
B. 303030
C. 292929
D. 282828
E. 272727
Solution:
416525=232525=271025=128â‹…10254^{16} 5^{25}=2^{32} 5^{25}=2^{7} 10^{25}=128 \cdot 10^{25}416525=232525=271025=128â‹…1025. Thus the usual form is 128128128 followed by 252525 zeros, for a total of 282828 digits.