In order to compensate for the non-linearity of an electronic device, an exponentiation conversion circuit that can change the power exponent to any value has been proposed. The exponentiation conversion circuit multiplies the logarithmically converted input signal by a power exponent value to perform exponential conversion. As a result, we can obtain the power function characteristic of a power exponent value. This circuit is a small-scale circuit that utilizes the exponential characteristics of the MOSFET subthreshold region. In a conventional circuit, expansion of the signal dynamic range and reduction of the power supply voltage have been an issue. In this paper, it was confirmed by simulation that the signal dynamic range has expanded by optimizing the current density of MOSFETs. In addition, the linearity of the multiplying circuit was improved by feedback produced by the operational amplifier circuits. We proposed reducing its power supply voltage from 6.0 to 3.3 V by a new multiplying circuit that can eliminate the restriction of maximum voltage gain. Our circuit expands its signal dynamic range from 17.5 to 42.7 dB in condition of the power exponent value from 0.50 to 2.0.