# Documentation

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# power, .^

Element-wise power

C = A.^B
C = power(A,B)

## Description

example

C = A.^B raises each element of A to the corresponding power in B.

C = power(A,B) is an alternate way to execute A.^B, but is rarely used. It enables operator overloading for classes.

## Examples

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Create a vector, A, and square each element.

A = 1:5;
C = A.^2
C = 1×5

1     4     9    16    25

Create a matrix, A, and take the inverse of each element.

A = [1 2 3; 4 5 6; 7 8 9];
C = A.^-1
C = 3×3

1.0000    0.5000    0.3333
0.2500    0.2000    0.1667
0.1429    0.1250    0.1111

An inversion of the elements is not equal to the inverse of the matrix, which is instead written A^-1 or inv(A).

Calculate the roots of -1 to the 1/3 power.

A = -1;
B = 1/3;
C = A.^B
C = 0.5000 + 0.8660i

For negative base A and noninteger B, if abs(B) is less than 1, the power function returns the complex roots of A.

Use the nthroot function to obtain the real roots.

C = nthroot(A,3)
C = -1

## Input Arguments

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Base, specified as a scalar, vector, matrix, or multidimensional array. Inputs A and B must either be the same size or have sizes that are compatible (for example, A is an M-by-N matrix and B is a scalar or 1-by-N row vector). For more information, see Compatible Array Sizes for Basic Operations.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64 | logical | char
Complex Number Support: Yes

Exponent, specified as a scalar, vector, matrix, or multidimensional array. Inputs A and B must either be the same size or have sizes that are compatible (for example, A is an M-by-N matrix and B is a scalar or 1-by-N row vector). For more information, see Compatible Array Sizes for Basic Operations.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64 | logical | char
Complex Number Support: Yes