In the present research, we investigate a novel type of exponential operator. This operator is developed using p(x) = x 4/3. Here, we establish the direct estimate, quantitative variants of the Voronovskaja theorem, same quantification for functions having exponential growth and some other convergence estimates for the newly defined exponential-type operator. Later in the end, we analyze graphically the convergence of the new operator for the exponential function e −4x .