Power (function)
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 This page describes the dyadic function. For the monadic function that uses 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
×/5⍴3
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 nth root of the base. For example, a right argument of ÷2
gives the square root.
3*2
9
9*÷2
3
Power has two inverses, Root and Logarithm:
2*3
8
2⍟8
3
3√8
2