Finding RMS current of BLDC motor
Is there a way to compute the RMS current from just the rated voltage and rated power values given?

No. We can compute the rated current however.
First, why we cannot. RMS (root-mean-square) is a method for creating an equivalent DC value for an arbitrary AC waveform.
&quot;RMS&quot; exists to compare AC voltage to DC voltage, since it is conceptually easier to deal with DC. Most AC voltages are RMS - i.e. 240VAC really means 240VAC RMS.
The wall outlet power may be 240VAC RMS, which means it will do exactly the same amount of work to a load if it were instead 240VDC. But the 240VAC is not DC - it an alternating wave! More than half of the time this alternating wave is near 0V, so the peaks must be much bigger than 240V for the RMS value to be the same. (These peaks are in fact \$\sqrt{2}\$ or 1.414 times bigger, so for 240VAC this will be 240*1.414 = 339V.)  We call this the &quot;peak&quot; voltage, or Vp, for &quot;voltage, peak.&quot; Since AC alternates, there are always two peaks, a positive one and a negative one.

[From Lessons in Electric Circuits by Tony Kuphaldt.]
As such, RMS operates on an actual waveform; the result of which is totally dependent on that waveform. (i.e., \$\sqrt{2}\$ only applies to a sinusoid; you'll get very different RMS numbers for a 339vp squarewave, or 339vp triangle wave, etc.)
In general, for a 50% duty-cycle squarewave, the RMS value is equal to VP.  So if a +/-72V supply is used, the RMS voltage is 72V. (The direction can be positive or negative, but is always one or the other and nothing else, so the net effective voltage is 72V.)

If using a +/-36V supply (72V in total), the RMS voltage is 36V.

Things get tricky with squarewaves when you change the duty cycle, which is likely the case with a variable-frequency BLDC motor driver. Depending on model, those can constantly change the duty cycle, so that the net voltage which reaches the motor legs approximates sinusoids. So the motor runs like it is being powered from AC, when actually it is being powered by thousands of carefully-timed DC current pulses every second.  So not only is there a roughly sinusoid-shaped average current to the motor, but zooming in, there are many small pulses every second.
Hopefully it is evident that accurately measuring the Watts (Volts x Amps) going to the motor is quite challenging. Typically this is done by monitoring the voltage and current going into one, two, or all three legs of the motor. Using ADC's or linear amplifiers, convert those (discrete) currents into RMS values.  Then multiply Vrms X Irms to get the instantaneous power. Typically this is coordinated via a microcontroller or CPU, and is used for over-current protection.
Now, to the question at hand: How many (rated) Amperes is a 72V 1500W motor?
Well this is straight Ohm's Law.  Watts = Volts * Amps.  We're given the 72V, so \$ 72\cdot I= 1500\$.  Dividing both sides by 72 to get I by itself, \$I=\frac{1500}{72}\$. The result is the (RMS!) current necessary to drive 1500W into that motor, while powered from 72V (RMS!)
Do note that this is rated current, not RMS current. If it's a 1500W motor, it is rated for the rated current. The RMS current must be measured, and can be any value up to the rated current.  The instantaneous current can go well beyond the rated current (think fast acceleration), but only for a short time.  Exceeding the 1500W RMS rating for too long will cause the motor to overheat and fail.