How many possible outcomes are there when flipping a coin 8 times

We know that flipping a coin has two outcomes, head or tail.
H
T
Flipping it twice gives two more outcomes for each of the previous outcomes, i.e.
HH
HT
TH
TT
Basically, it doubles the number of outcomes for every extra flip, which is also the result of the multiplication rule.

For n flips, the number of outcomes is 2^n.
This answer applies when order counts, which is implied by "flipping 8 times."

Note:
If we flip 8 coins (i.e. together), there are only 9 outcomes, i.e. from 0 to 8 heads.  This is the case when order does not count.