Hive is Hive and HP is Hive Power, your Hive Power is the same amount of Hive irrespective of the actual dollar price of Hive.
Ten Hive powered up when the value is 20c say and Ten Hive powered up when the price is 40c is still 10 HP although the dollar value will be 2 dollars and 4 dollars, the HP is still 10.
The only time the dollar amount affects anything is when you take Hive off chain. On Hive it does not matter what the value is, 1 Hive is 1 Hive, where there is a difference is in the Hive Backed Dollar. So for example when we have a love $ value of Hive, then we can get more Hive when we swap our HBD...
Does that help?