Layman’s terms:
It all comes down to "rated" power of your amplifier across the impedance of your speakers, with high emphasis over the bottom KHz or so.
Note I said across impedance, and not just at the lowest impedance as is often brought up. While a 4 ohm speaker may drop to 2 ohms (or less), it may also go up to 10 or 12 ohms (or higher) and do that over a relatively narrow frequency range. At a given volume level, not being able to deliver the required voltage at the impedance peaks or the current at impedance minimums will both cause issues in sound.
We next get into continuous ratings and peaks ratings. There are US and international standards for peak ratings. Are they good enough? Questionable, but nothing is stopping anyone from over designing beyond the standards with oversized transformers and/or large capacitor banks (or an architecture that allow more power supply droop). Of course you need high enough power supply voltages and beefy enough power supply to support the music peaks at the impedance peaks (which can be where heavy bass occurs), and a beefy enough output stage (and power supply) to support the current peaks and the minimum impedance, which are pretty much always bass.
From above .... beefy supply is the first need independent of the speaker requirements, and if your speaker dips low in impedance, you need a beefy output stage too, .... and there are many architectures that have been created to allow higher short term power bursts as is required for real music, but does not improve continuous power ratings.
So can you tell the "power" from the specs .... maybe. Depend on whether the amplifier vendor provides you enough details and you know enough about your speakers. That is about as easy as one can make it.
It all comes down to "rated" power of your amplifier across the impedance of your speakers, with high emphasis over the bottom KHz or so.
Note I said across impedance, and not just at the lowest impedance as is often brought up. While a 4 ohm speaker may drop to 2 ohms (or less), it may also go up to 10 or 12 ohms (or higher) and do that over a relatively narrow frequency range. At a given volume level, not being able to deliver the required voltage at the impedance peaks or the current at impedance minimums will both cause issues in sound.
We next get into continuous ratings and peaks ratings. There are US and international standards for peak ratings. Are they good enough? Questionable, but nothing is stopping anyone from over designing beyond the standards with oversized transformers and/or large capacitor banks (or an architecture that allow more power supply droop). Of course you need high enough power supply voltages and beefy enough power supply to support the music peaks at the impedance peaks (which can be where heavy bass occurs), and a beefy enough output stage (and power supply) to support the current peaks and the minimum impedance, which are pretty much always bass.
From above .... beefy supply is the first need independent of the speaker requirements, and if your speaker dips low in impedance, you need a beefy output stage too, .... and there are many architectures that have been created to allow higher short term power bursts as is required for real music, but does not improve continuous power ratings.
So can you tell the "power" from the specs .... maybe. Depend on whether the amplifier vendor provides you enough details and you know enough about your speakers. That is about as easy as one can make it.