Is there an exponentiation configuration for MOSFETs or Opamps?
Look up the square root diode function circuit,  but modify for higher current maybe using  a 3x Darlington emitter follower. This drives an unity inverter Op Amp 1st stage with emitter follower feedback for current gain to drive the 2nd stage inverting square root circuit for non-INV sqrt. sqrt function where \$Vout=k\sqrt{Vin}=k\sqrt{Pd*Rin} \$, where R input resistor accepts the high current to achieve the constant power or quadratic voltage of  base-emitters before saturation, where it becomes more linear.  Here the intermediate input R receives the current and the op amp Vin+ ref =0 but needs two inv. stages to make a non inverting function from a high impedance source.  

If you have a low impedance source input that can drive this current, then use the 1st stage on the output which is needed to provide linear voltage gain to make k * k2=1 since k is limited due to the voltage range of 3 Vbe’s in a triple Darlington from 0 to 1.5Vish volts or maybe use 2 Darlingtons for a 2V range or a linear voltage gain circuit.

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Here is one example where labelled R values are equal for k=1 but others must be chosen not to allow output currents to saturate the Op Amp or the Vce=0 which limits the decades of range unless you inject clever offsets that cancel/avoid this.