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A multiplicative monoid defines the property of exponentiation with ________

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A multiplicative monoid defines the property of exponentiation with ________

(a) integer exponents

(b) fractional exponents

(c) rational exponents

(d) negative integer exponents

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This interesting question is from Number Theory in chapter Number Theory and Cryptography of Discrete Mathematics

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The correct choice is (a) integer exponents

Explanation: Exponentiation with integer exponents is termed in any multiplicative monoid. Exponentiation is described inductively by 1) h^0 = 1 for all h ∈ S, h^n+1 = h^n h and non-negative integers n, If n is a negative integer then h^n is only defined if h has an inverse in S. Monoids define many structures including groups and rings (under multiplication).

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