When multiplication is repeated, the resulting operation is known as **exponentiation**. For instance, the product of three factors of two (2×2×2) is "two raised to the third power", and is denoted by 23, a two with a superscript three. In this example, the number two is the **base**, and three is the **exponent**. In general, the exponent (or superscript) indicates how many times to multiply base by itself, so that the expression

indicates that the base *a* to be multiplied by itself *n* times.

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### Other articles related to "exponentiation":

Hyperoperation

... then continues with the binary operations of addition, multiplication and

... then continues with the binary operations of addition, multiplication and

**exponentiation**, after which the sequence proceeds with further binary operations extending beyond**exponentiation**, using right-associ ... For the operations beyond**exponentiation**, the nth member of this sequence is named by Reuben Goodstein after the Greek prefix of n suffixed with -ation (such as tetration, pentation) and can ...Complex Numbers Exponential - Generalizations - In Abstract Algebra

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**Exponentiation**for integer exponents can be defined for quite general structures in abstract algebra ... written additively, as it often is for abelian groups, then "**exponentiation**is repeated multiplication" can be reinterpreted as "multiplication is repeated addition" ... Thus, each of the laws of**exponentiation**above has an analogue among laws of multiplication ...Abuse Of Notation - Examples -

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**Exponentiation**As Repetition...

**Exponentiation**is repeated multiplication, and multiplication is frequently denoted by juxtaposition of operands, with no operator at all ...**Exponentiation**over sets ...Complex Numbers Exponential - Generalizations - Over Sets

... This is sometimes written κA to distinguish it from cardinal

... This is sometimes written κA to distinguish it from cardinal

**exponentiation**, defined below ... If the base of the**exponentiation**operation is a set, the**exponentiation**operation is the Cartesian product unless otherwise stated ... functions from N to S in this case This fits in with the**exponentiation**of cardinal numbers, in the sense that**Exponentiation**- History of The Notation

... Nicolas Chuquet used a form of exponential notation in the 15th century, which was later used by Henricus Grammateus and Michael Stifel in the 16th century ... Samuel Jeake introduced the term indices in 1696 ...

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