(2.5×108)(8×107)

Multiply the 2.5×8 and get 20. 
Add the exponents 8+7 and get 15

So that becomes

20×1015

However, that is not in scientific notation
because the 20 is not between 1 and 10.  So
we get 20 in scientific notation as 2×101,
Then we replace the 20 by 2×101:

2×101×1015

and we add the exponents and end up with

2×1016

Edwin