Just for clairification, the property is xmax, not wmax
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Think of an amp as a car engine. Cruising around town doesn't require much power. But accelerating to reach highway speed will require much more, as well as show if your car is underpowered.
The issue with underpowering speakers is that they can be damaged when an amp is driven into clipping. This will occur when trying to achieve higher and higher sound levels. At moderate levels, speakers will essentially sound the same if the amps are operating within thier limits. If you have a large room or inefficient speakers, more power will be required to reach the same spl. This increases the demands on the amp and makes clipping more likely.
Most of the time, only a couple watts will be used (continuously). In your case, there probably won't be a noticible difference between 130 watts and 500 watts as you will not be using the reserve power (except on dynamic peaks). Many speaker power ratings are also misleading, as a speaker can fail in several different ways.
Basically, it will be fine to use a lower power amp as long as you're responsible with the volume control. Just turn it down if you hear distortion. More power will give you better dynamics and more reserve, which are both good things.