Well, in the US Alpha space starts at 18000. So, in theory, I can climb, uncontrolled and without talking to anyone, under VFR all the way to 17999 ... then Alpha starts and you need to be IFR up there (meaning, IFR certified and under an IFR flight plan).
I know that other countries have it different ... "transition levels" I think they are called and they start anywhere between 6000 and 10000 depending on the country.
Yeh my cherokee has 180hp ... but it's a heavy bird. It's 1600 empty and it grosses at 2500 which means that on a hot summer day I gotta wrestle it off the ground a little (if I have 3 people on board ... 4 people, forget it. it won't even lift off).