Exponentialsign

Exponentialsign is a notational construct used in some mathematical and computer algebra contexts to combine an exponent and its sign into a single token. In its simplest form, Exponentialsign(b, s, n) denotes the value b^(s n), where b > 0, n is a real number, and s is a sign indicator equal to +1 or -1. This compact notation is intended to streamline expressions that repeatedly use signed exponents or to simplify automated generation of exponent expressions in symbolic systems.

Examples help illustrate the idea: Exponentialsign(3, +, 2) equals 9, Exponentialsign(2, −, 3) equals 1/8, and Exponentialsign(4, −, 1.5) equals 4^(−1.5) which equals 1/8. Note that with negative bases or non-integer exponents, real results require appropriate restrictions (for example, real-valued outputs are straightforward for positive bases and real exponents; otherwise complex results may arise).

As a notational device, Exponentialsign does not introduce a new algebraic operation; it simply encodes a signed exponent in a compact form. It adheres to the usual laws of exponents: for the same sign, Exponentialsign(b, s, n) * Exponentialsign(b, s, m) equals Exponentialsign(b, s, n+m). If the signs differ, the product follows standard exponent rules and can be expressed as b^(n−m) or b^(m−n) depending on the order. The notation is primarily a convenience in teaching materials and some symbolic-computation frameworks, rather than a widely adopted mathematical standard.

Related topics include exponentiation, the exponential function, and sign notation.