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Exponentiation
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==Repeated exponentiation== {{Main|Tetration|Hyperoperation}} Just as exponentiation of natural numbers is motivated by repeated multiplication, it is possible to define an operation based on repeated exponentiation; this operation is sometimes called hyper-4 or tetration. Iterating tetration leads to another operation, and so on, a concept named [[hyperoperation]]. This sequence of operations is expressed by the [[Ackermann function]] and [[Knuth's up-arrow notation]]. Just as exponentiation grows faster than multiplication, which is faster-growing than addition, tetration is faster-growing than exponentiation. Evaluated at {{math|(3, 3)}}, the functions addition, multiplication, exponentiation, and tetration yield 6, 9, 27, and {{val|7625597484987}} ({{math|1==3<sup>27</sup> = 3<sup>3<sup>3</sup></sup> = <sup>3</sup>3}}) respectively.
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