[Jshwaa]

mAh has nothing to do with increasing power

You are wrong. The very definition of electrical power can be equated to current times voltage.

Higer mAh = longer runtime, higher voltage and discharge rating = speed/torque/power

How the heck does higher mAh amount to higher voltage? Also, you just contradicted yourself. You were quoted as stating that mAh has nothing to do with increasing power, and then quoted as saying it does. Make up your mind.

A 3000mAh cell will NOT give more power than a 500mAh cell unless the former has a higher discharge rating.

Ok, I challenge you to find 2 cells of the same chemistry(li-ion, nimh, nicd, etc.) with a higher mAh rating but lower discharge rating. You won't. Cell's discharges are rated in "C". The C is a multiplier. You multiply the C by the mAh rating to get the discharge rate. Therefore if a cell has higher mAh, it has higher discharge rate.

You are correct about 9v batteries having poor perfromance, but for the wrong reason. 9v batteries have a relatively low discharge rating (c rating).

Now what did I say? mAh of cells equates to discharge rates in that if you have a higher mAh rating, you have a higher discharge rate. The reason 9V have low discharge rates is because a 9V is composed of 6 tiny 1.5V cells in series. Each of these tiny cells have a very small mAh rating. The discharge rate of the 9V is dictated by the small mAh rating of the 6 small cells. Also, cells have an internal resistance. Putting cells in series puts the cells resistances in series, thus lowering the discharge rate even more.

I don't know who you are, but you're clueless in your attempt at saying I was wrong at anything. I would just give it up if I were you.