7.3. Kolya wants to multiply all the natural divisors of the number 1024 (including the number itself) on his calculator. Will he be able to get the result on a screen with 16 decimal places?
Answer: It will not be able to... The natural divisors of the number $1024=2^{10}$ are the numbers $1,2^{1}, 2^{2}, \ldots, 2^{10}$. Their product is $2^{1+2+\ldots+10}=2^{55}$. Since $2^{10}=1024>10^{3}$ and $2^{5}=128>10$, then $2^{55}=\left(2^{10}\right)^{5} \cdot 2^{5}>\left(10^{3}\right)^{5} \cdot 10=10^{16}$, i.e., $2^{55}$ is written using no fewer than 17 digits.