In this paper, we defined and studied the concept of exponential type multiplicatively convex functions and some of their algebraic properties. We derived Hermite-Hadamard inequalities for this class of functions. We also established new Hermite-Hadamard type inequalities for the product and quotient of exponential type multiplicatively convex functions. In addition, we obtained new multiplicative integral-based inequalities for the quotient and product of exponential type multiplicatively convex functions and convex functions. The results in this study could potentially inspire further research in various scientific fields.