Definition:Power (Algebra)/Exponent

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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)