3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 = 3 ^ 9
Do yo mean that there are 9 differently colored bottles, and you need to enumerate the ways to choose 3 among these and put them in a line?
Then it would be : 9 choices for the first bottle in the line, 8 for the second (it can't be the first), and finally 7 choices for the third bottle.