^^^ What Tim said. Why my initial response to the question was 25 words or less as one could easily write a doctoral dissertation on the topic. (Not being sarcastic at all - fact)
In general what Tim alluded to is the correct way to do it. Amplifier ratings, given an ethical manufacturer of professional grade equipment ( a whole chapter could be written on this) rate power on the amps is in continuous. However, it's not continuous "continuous", it's continuous over a specified period of time - generally, there again would probably be exceptions.
Simply put it works pretty much like this. Go past continuous power ratings of speakers with them amp with the mind set of "peak" the speakers will handle and put an amp that will deliver that means you're letting the amp somewhat cruise and putting the drivers are their maximum.
What happens, when we go up the hill past "nominal" power input to a
speaker/amp. Well for the speaker it just shortens the lifespan. Depending upon how hard it's driven with music program. Then can be literally beat to and early death. Meaning mechanical failure in
the voice coil bond to the cone or diaphragm. Or, mechanical failure due to over-excursion in LF drivers at the lower end of the bandwidth.
Drive them harder and longer and it typically becomes a contest of which failure mode will manifest first, typically it will be voice coil burnout.
We haven't mentioned "power compression" which is simply the fact that electrical input -vs- acoustic output is not linear throughout it's operating range. At the high end they manifest power compression, whereas output power is no longer tracking with increases of input power.
So, for optimal performance over lifetime, and getting the most bounce for the ounce on what comes out of the back of the truck, a close to even match between amplifier and speaker is usually the best solution.
In a system under construction I am going to drive JBL 2269 18's with Crown MA-5000i's. The lower end of the power rating for the JBL subs, however they will be at optimal efficiency, not as subject to over excursion at the low end - AND, the price I got the like new condition Crown MA5000i's makes the business case solid. Pushing the subs with that power range they will live long and prosper.
That choice when posted, there are those out there that will claim they are under-powered and can handle more. Probably so, at the trade-off of a shorter lifespan and more amplifier expense.
Business case model for me say's I hit the sweet spot.
It took me a few trips to the technician's service bench with amplifiers with wasted output devices and speaker recone jobs to learn this.
The other part is system setup, gain structure and limiters to optimize performance for maximum safe output levels. Building the Ferrari is one thing, then you need to learn how to drive it to get the best lap times and not destroy it (into the wall or another car, wear out tires, burn through fuel, blow engine, destroy transmission) before the race ends.
The seasoned audio engineer is just like a crew chief on a race car.
As Carl stated, he buys at the higher power rating for the amps and doesn't drive them as hard. Solid practice, he knows not the drive the amps full tilt - doing that will shorten lifespan on the drivers. My case was the other end and I looked at the business case as well and the bang-for-buck deal on the MA-5000i's and went that way. I'll drive the amps up to the region of rated power. They're solid amps and will handle that just fine over the long haul.
Basically, when doing system design and matching amp power to drivers - just know what choices you made and why, and sometimes it will influence system setup decisions. There is no single "right answer". It can be approached from a "run what you brung", "optimum design" or "business case" perspective that will all yield good results - the best choice being the one that fits the situation.
