When the integer $300^{8}$ is written out, it has $d$ digits. What is the value of $d$ ?
We note that $300^{8}=3^{8} \cdot 100^{8}=3^{8} \cdot\left(10^{2}\right)^{8}=6561 \cdot 10^{16}$.

Multiplying 6561 by $10^{16}$ is equivalent to appending 16 zeroes to the right end of 6561 , creating an integer with 20 digits.