How many digits are there in $2^{17}\times 3^2\times 5^{14}\times 7 ?$

Question

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???

Answer 1

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

Answer 2

If we selectively combine terms as we evaluate:

$$2^{17} \times 3^2 \times 5^{14} \times 7 = 10^{14} \times 2^3 \times 3^2 \times 7$$

$$ = 10^{14} \times 504$$

In particular, $$10^{16} < (10^{14} \times 504) < 10^{17}$$

I'll let you fill in the details. :)