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# power, .^

Element-wise power

## Syntax

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

## Description

example

````C = A.^B` raises each element of `A` to the corresponding powers in `B`. The sizes of `A` and `B` must be the same or be compatible.If the sizes of `A` and `B` are compatible, then the two arrays implicitly expand to match each other. For example, if one of `A` or `B` is a scalar, then the scalar is combined with each element of the other array. Also, vectors with different orientations (one row vector and one column vector) implicitly expand to form a matrix.```
````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)`.

Create a 1-by-2 row vector and a 3-by-1 column vector and raise the row vector to the power of the column vector.

```a = [2 3]; b = (1:3)'; a.^b```
```ans = 3×2 2 3 4 9 8 27 ```

The result is a 3-by-2 matrix, where each (i,j) element in the matrix is equal to a`(j) .^ b(i)`:

`$\mathit{a}=\left[{\mathit{a}}_{1}\text{\hspace{0.17em}}{\mathit{a}}_{2}\right],\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\mathit{b}=\left[\begin{array}{c}{\mathit{b}}_{1}\\ {\mathit{b}}_{2}\\ {\mathit{b}}_{3}\end{array}\right],\text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}\text{\hspace{0.17em}}\mathit{a}\text{\hspace{0.17em}}.ˆ\text{\hspace{0.17em}}\mathit{b}=\left[\begin{array}{cc}{{\mathit{a}}_{1}}^{{\mathit{b}}_{1}}& {{\mathit{a}}_{2}}^{{\mathit{b}}_{1}}\\ {{\mathit{a}}_{1}}^{{\mathit{b}}_{2}}& {{\mathit{a}}_{2}}^{{\mathit{b}}_{2}}\\ {{\mathit{a}}_{1}}^{{\mathit{b}}_{3}}& {{\mathit{a}}_{2}}^{{\mathit{b}}_{3}}\end{array}\right].$`

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`, the `power` function returns complex results.

Use the `nthroot` function to obtain the real roots.

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

Since R2023a

Create two tables and raise the first table to the power of the second. The row names (if present in both) and variable names must be the same, but do not need to be in the same orders. Rows and variables of the output are in the same orders as the first input.

`A = table([1;2],[3;4],VariableNames=["V1","V2"],RowNames=["R1","R2"])`
```A=2×2 table V1 V2 __ __ R1 1 3 R2 2 4 ```
`B = table([4;2],[3;1],VariableNames=["V2","V1"],RowNames=["R2","R1"])`
```B=2×2 table V2 V1 __ __ R2 4 3 R1 2 1 ```
`C = A .^ B`
```C=2×2 table V1 V2 __ ___ R1 1 9 R2 8 256 ```

## Input Arguments

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Operands, specified as scalars, vectors, matrices, multidimensional arrays, tables, or timetables. `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.

• Operands with an integer data type cannot be complex.

Inputs that are tables or timetables must meet the following conditions: (since R2023a)

• If an input is a table or timetable, then all its variables must have data types that support the operation.

• If only one input is a table or timetable, then the other input must be a numeric or logical array.

• If both inputs are tables or timetables, then:

• Both inputs must have the same size, or one of them must be a one-row table.

• Both inputs must have variables with the same names. However, the variables in each input can be in a different order.

• If both inputs are tables and they both have row names, then their row names must be the same. However, the row names in each input can be in a different order.

• If both inputs are timetables, then their row times must be the same. However, the row times in each input can be in a different order.

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

## More About

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### IEEE Compliance

For real inputs, `power` has a few behaviors that differ from those recommended in the IEEE®-754 Standard.

MATLAB® IEEE

`power(1,NaN)`

`NaN`

`1`

`power(NaN,0)`

`NaN`

`1`

## Version History

Introduced before R2006a

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