Power (function)

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This page describes the dyadic function. For the monadic function that uses $e$ as a base, see Exponential. For the iteration operator, see Power (operator).
 *

Power (*) is a dyadic scalar function that computes the exponentiation function of the two arguments, so that X*Y is X raised to the power Y. Power shares the glyph * with the monadic arithmetic function Exponential.

Examples

2*¯1 0 1 2 3 4 5
0.5 1 2 4 8 16 32

A common technique is to choose sign based on a Boolean array:

¯1*1 0 0 1 0
¯1 1 1 ¯1 1

Properties

For positive integer Y, X*Y equals the product of Y copies of X. When Y is 0, X*Y equals 1, possibly except when X is also 0 (since zero to the power of zero is undefined in mathematics).

3*5
243
×/53
243
1 2 3*0
1 1 1

Negating the exponent (right argument) gives the reciprocal of the return value.

(2*¯4)2*4
1

If the exponent is the reciprocal of some number n, the result is the n-th root of the base. For example, a right argument of ÷2 gives the square root.

3*2
9
92
3

Power has two inverses, Root and Logarithm:

2*3
8
28
3
38
2