# Definition:Power (Algebra)/Exponent

< Definition:Power (Algebra)(Redirected from Definition:Index (Algebra))

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## Definition

In the **power operation** $x^r$, the number $r$ is known as the **exponent of $x$**, particularly for $r \in \R$.

## Examples

### Example: $2^2$

In the expression:

- $2^2$

the **exponent** is $2$ (the second one), while the second power of $2$ is $4$.

## Also known as

The **exponent** of a **power operation** is also called the **index** (plural **indices**).

Sometimes **power** is used to mean the **exponent**, but strictly speaking **power** refers to the result of the operation.

## Also see

- Results about
**exponents**can be found**here**.

## Sources

- 1997: Donald E. Knuth:
*The Art of Computer Programming: Volume 1: Fundamental Algorithms*(3rd ed.) ... (previous) ... (next): $\S 1.2.2$: Numbers, Powers, and Logarithms: $(4)$ - 1998: David Nelson:
*The Penguin Dictionary of Mathematics*(2nd ed.) ... (previous) ... (next):**exponent (index)** - 1998: David Nelson:
*The Penguin Dictionary of Mathematics*(2nd ed.) ... (previous) ... (next):**index**(*plural***indices**)**${}$**:**2.** - 2008: David Nelson:
*The Penguin Dictionary of Mathematics*(4th ed.) ... (previous) ... (next):**exponent (index)** - 2008: David Nelson:
*The Penguin Dictionary of Mathematics*(4th ed.) ... (previous) ... (next):**index**(*plural***indices**)**${}$**:**2.** - 2014: Christopher Clapham and James Nicholson:
*The Concise Oxford Dictionary of Mathematics*(5th ed.) ... (previous) ... (next):**index (indices)**