Evaluate numerically:

Evaluate to high precision:

Efficiently compute the first million digits of a result:

Complex numbers are generated when necessary:

The principal root is always used:

This follows from the general definition of Power as :

Surd can be used to get the real root:

Complex number inputs:

Power threads elementwise over lists and matrices:

Power can be used with Interval and CenteredInterval objects:

Compute average-case statistical intervals using Around:

Compute the elementwise values of an array:

Or compute the matrix Power function using MatrixFunction:

Values at zero:

Depending on the real part of , the result can be 0 or infinity:

Hence the following is indeterminate:

Limiting values at infinity:

Evaluate symbolically:

Find a value of x for which the Power[x,3]=0.5:

Visualize the result:

Plot the function over the reals for several integers n:

Plot the real and imaginary parts of over the reals:

Compare the real and imaginary parts of (Power[x,]) and (CubeRoot[x]) over the reals:

Plot the real part of :

Plot the imaginary part of :

Polar plot with :

is defined for all real when :

It is only defined for integer when :

For nonzero complex , it is an entire function of :

Function range of :

Power is right-associative:

The form on the right-hand side is the preferred form:

Power is periodic in its second argument in the complex plane:

Find limits at branch cuts:

For fixed, positive integer , is an analytic function of :

It is not analytic, but it is still meromorphic for negative integers :

For noninteger , it is not even meromorphic:

For a fixed, nonzero real , is an analytic function of :

As a bivariate function, is neither analytic nor meromorphic:

For , is increasing:

It is decreasing for :

is injective except for :

Visualize for :

is not surjective onto the reals for any value of :

Visualize for :

is positive for :

is non-negative for even :

has in general singularities for or for :

However, it is continuous at when :

is convex for :

is convex for positive even :

First derivative with respect to x:

Higher derivatives with respect to x:

Plot the higher derivatives with respect to x:

Formula for the derivative with respect to x:

Derivative with respect to its second argument:

The derivative:

Compute the indefinite integral using Integrate:

Verify the anti-derivative:

Definite integral:

More integrals:

Find the Taylor expansion using Series:

Plots of the first three approximations around :

General term in the series expansion using SeriesCoefficient:

The first-order Fourier series:

Taylor expansion at a generic point:

Primary definition:

Euler's formula:

Connection with Exp function:

Nested powers are not always automatically combined:

Use PowerExpand to force cancellation:

This can produce incorrect results:

Alternatively, use Simplify with appropriate assumptions:

Products are automatically combined:

Expand assuming real variables x and y: