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)