Lets break it down into a easier way to explain it.
If we could see one individual radio wave, we would be able to draw a line ( carrier ) though the center and the upper side band ( the radio wave above the carrier ) would be above the carrier and the lower side band ( the radio wave below the carrier ) would be below the carrier.

When we subtract one of the carriers, the forward power is transferred into the other band.
Now the carrier is a power hog and probably wastes 60% of the transmitted power.
So at that rate - if both side bands combined had 5 watts and you removed one of the side bands - you would effectively double the transmit power.

However, you have to account for losses, the loss of the connectors, the loss in the coax, the values of all the components in the radio, to be conservative lets say it is 12 watts PEP when it is new.

PEP stands for Peak Envelope Power.
http://en.wikipedia.org/wiki/Peak_envelope_power

The PEP output of an AM transmitter at full modulation is four times its carrier PEP; in other words, a sold-state, 100-watt amateur transceiver is usually rated for no more than 25 watts carrier output when operating in AM

When you turn on a vac cleaner, at the initial start up, you have a power spike which is needed to start the motor turning, that can be considered a peak power level. When manufactures sells a vac cleaner, they include the PEP power level to make the motor seem more impressive.

On the other hand, a VOM meter reads Root Mean Square - RMS power.
http://en.wikipedia.org/wiki/Root_mean_square

Because of their usefulness in carrying out power calculations, listed voltages for power outlets, e.g. 120 V (USA) or 230 V (Europe), are almost always quoted in RMS values, and not peak values.
Peak values can be calculated from RMS values from the above formula, which implies Vp = VRMS × √2, assuming the source is a pure sine wave.
Thus the peak value of the mains voltage in the USA is about 120 × √2, or about 170 volts.
The peak-to-peak voltage, being twice this, is about 340 volts.
A similar calculation indicates that the peak-to-peak mains voltage in Europe is about 650 volts.
It is also possible to calculate the RMS power of a signal. By analogy with RMS voltage and RMS current, RMS power is the square root of the mean of the square of the power over some specified time period.
This quantity, which would be expressed in units of watts (RMS), has no physical significance.
However, the term "RMS power" is sometimes used in the audio industry as a synonym for "mean power" or "average power".