Hi there! Thank you for the opportunity to help you with your question!
First, let's look at the number of sig figs from each term: 6.022 has four significant figures, whereas 1.05 has 3. Both 10^23 and 10^8 are actually placeholders for the other two values, so they are not considered.
Now, for multiplications, we perform the regular multiplication 6.022 * 1.05 = 6.3231, but we only keep as many significant figures as our lowest significant term, in this case 3 sig figs, from 1.05. So our product is 6.32 with 3 s.f.
We just have to multiply the placeholders now 10^23 * 10^8 = 10^31, so our final answer is 6.32 x 10^31, and i t has 3 sfs
Please let me know if you need any clarification. Always glad to help!