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In this paper, we derive an expression for the power of a nondiffracting microstructured vector light beam characterized by a continuous superposition of zeroth order ideal Bessel beams, known in the literature as Frozen Wave. Our final result expresses the power in terms of the spectrum of the Frozen Wave in the spatial frequency domain. The power evaluated from our final result is in accordance with that obtained by numerically integrating the average energy flux associated with the beam. Besides, our expression is less computationally demanded, which facilitates the determination of the optical forces produced by this vector light beam.