# Documentation

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# power, .^

Element-wise power

## Syntax

• ``C = A.^B``
example
• ``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 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 = 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

## More About

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### Tall Array Support

This function fully supports tall arrays. For more information, see Tall Arrays.

## See Also

#### Introduced before R2006a

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