How many digits are there in $$2^{17}\times 3^2\times 5^{14}\times 7 ?$$
Question added:
I agree with the fellow who asked that if one cannot have 2 and 5 in the number above how we will calculate the number of digits???
[Math] How many digits are there in $2^{17}\times 3^2\times 5^{14}\times 7 ?$
decimal-expansionelementary-number-theory
Best Answer
See if I multiply $2$ and $5$, I will get $10$. So $2^{14} $ and $5^{14}$ when multpilied will give $10^{14}$ which has 14 zeroes. All that remains to be multiplied is $8$ , $9$ and $7$, which is three digits when done. I already had $14$ digits. In total $17$ digits