Operative exponents

This research paper introduces a new mathematical framework called Operative Exponents, which generalizes the concept of exponents beyond traditional multiplication-based powers. The paper defines five types of operative exponents: Additive Exponents (A): repeated addition of a base number. Subtractive Exponents (S): repeated subtraction of a base number. Multiplicative Exponents (M): standard repeated multiplication. Division Exponents (D): repeated division of a base number. Expressive Exponents (E): advanced exponentiation using the Delton operator (∆9) to compress repeated symbolic expressions efficiently. The Delton operator (∆9) is introduced to simplify and compact symbolic representations of repeated operations, allowing concise expressions for complex formulas. The paper also establishes laws governing expressive exponents, including addition, subtraction, multiplication, and combined operations. This framework offers a new perspective in symbolic computation, algebraic manipulation, and theoretical mathematics. It provides potential applications in computational mathematics, advanced algebra, and mathematical modeling.