To extend the above remarks, your use of the term power, talking about a larger chainwheel or smaller cog, and your reference to climbing and acceleration don't make sense at all, especially when put together.
- The amount of power has nothing to do with gear combination or ratio. Power is the amount of work done (mass x distance) per unit of time. In other words, moving the same weight the same distance in less time (more speed) is more power.
- A larger chainwheel or smaller cog both increase gear ratio. Gears are essentially spinning levers, and the higher the gear ratio the longer is the distance between the pivot/fulcrum and the load. A longer distance toward the load (less toward you) means you can move the load much more/faster with a given movement on your part, but it also means you have to exert much more force to do so. So a higher gear will only mean faster speed if you are stronger (or more efficient).
- Acceleration and climbing both require lower gears. Technically if you are going 5 mph on the flat and keep that speed up a hill you are accelerating according to the meaning in physics.
If you are wanting higher gears there's a good chance you are already riding higher gears than is advisable in order to reach your goal of more speed/power. For a variety of reasons it is better to
first adopt a higher crank spin rate (coupled with a lower gear) on a bike - generally above 75rpm or so - both to go faster and to get faster. You can also increase the power delivered to the pedals in relationship to your effort by making sure the bike is set up so as to be as efficient as possible for your body dimensions.
Incidentally, differences in bike/component weight, tire rolling resistance, stiffness of frame, etc. all pale next to the engine when it comes to better performance on a bike.