To solve this problem with have to follow the order of operations. (PEMDAS) Parenthesis, Exponents, Multiply, Divide, Add, Subtract.
We'll start with the first set of parenthesis.
(6.02*10^23)
10^23 = 1e+23 (1 followed by 23 zeroes)
6.02*1e+23 = 6.02
Now we'll solve the second set of parenthesis.
(8.65*10^4)
10^4 = 10,000
8.65 * 10,000 = 86,500
Now onto the final step. We multiply together both numbers.
6.02 * 86,500 = 520,730