I've searched the web for this but haven't found a conclusive answer. Most answers indicated that it is possible. So, Can I use Power Attack with light weapons? If it can be done, why does this feat exist;
Piranha Strike (Combat)
You make a combination of quick strikes, sacrificing accuracy for
multiple, minor wounds that prove exceptionally deadly.
Weapon Finesse, base attack bonus +1.
Benefit: When wielding a light weapon, you can choose to take a -1
penalty on all melee attack rolls and combat maneuver checks to gain a
+2 bonus on all melee damage rolls. This bonus to damage is halved (-50%) if you are making an attack with an off-hand weapon or
secondary natural weapon. When your base attack bonus reaches +4, and
for every 4 points thereafter, the penalty increases by -1 and the
bonus on damage rolls increases by +2. You must choose to use this
feat before the attack roll, and its effects last until your next
turn. The bonus damage does not apply to touch attacks or effects that
do not deal hit point damage. This feat cannot be used in conjunction
with the Power Attack feat.
Check the prerequisites. Power Attack needs a Strength 13, while Piranha Strike needs Weapon Finess, which is interesting only if your Dex is greater than you Str, so we can deduce that the latter is intended for Dexterity-oriented characters, the fluff text incidentally says one using Piranha Strike provokes "multiple, minor wounds".
For a more complete answer, Power Attack doesn't say anything about light weapons, but it does say that you can use this feat with a natural weapon, and natural weapons are considered light weapons.
Besides, if you couldn't use Power Attack with a light weapon, the description of the Piranha Strike feat wouldn't explicitly tell that