For a nonnegative integer exponent, exponentiation iterates multiplication: and . This convention defines in primitive recursive arithmetic. Extensions to other exponents may use different domains and conventions.
The hyperoperation hierarchy successively iterates basic arithmetic operations. In the usual indexing, successor is followed by addition, multiplication, exponentiation and their higher iterates. A sequence beginning with addition shifts this index by one. Each fixed rank is a primitive recursive function; this does not imply that the evaluator taking the rank as an additional variable is primitive recursive.
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Exponentiation is a mathematical operation that involves raising a number, called the base, to the power of an exponent. The exponent indicates how many times the base is multiplied by itself. The operation can be expressed in the form: \[ a^n \] where: - \( a \) is the base, - \( n \) is the exponent.
