Verified Answer :

\(8.4*10^2*2.5*10^6\to\boxed{21*10^8}\)

(8.4 10^2) (2.5 10^6)
associative property -> we can multiply these in whichever order we want
8.4 2.5 10^2 10^6
21
10^8
if your instructions said to put the answers in scientific notation, however, we are not done here
21 10^8
2.1
10 10^8
2.1
10^9