So the power required at 150 KIAS at FL300 will be approximately 1.5 cubed = 3.375 times the power required at 150 KIAS at 5000 feet.
Dodgy? How do you actually measure "power"?
Blogg's jet science: Drag requires Energy to be used = fuel burnt. Drag, roughly speaking, is
mostly created by IAS.
At 250KIAS at Sea Level (TAS around 250), I use about 2100kg/per hour. N1 is way down, around 60%
At 250KIAS at FL300, I will still use around 2100kg/hr, but TAS is around 400. N1 is way up, around 85%.
If 3.375 times the power is required at FL300, there would be no point in going high at all. You only get a 80% increase in speed. Far cheaper (but longer) to fly low.