Expand a square root, implicitly assuming positive real values:

Without PowerExpand, no expansion is done:

The expansion is only correct for positive real variables:

This gives a completely correct result:

This gives a result correct under the specified assumptions:

Expand a power of a product; the result may not be correct everywhere:

The general formula for expanding a power of a product:

Expand nested powers; the results may not be correct everywhere:

General formulas for expanding a nested power:

Expand the logarithm of a power; the result may not be correct everywhere:

The general formulas for expanding logarithms of powers:

Expand the logarithm of a product; the result may not be correct everywhere:

The general formula for expanding the logarithm of a product:

Expand compositions of inverse trigonometric and trigonometric functions:

This gives the universally correct formula:

Compute an expansion valid under the specified assumptions:

Expand the argument of a product:

Expand only with respect to a and b:

Find universally correct expansion rules:

Expand under specified assumptions:

PowerExpand performs expansions valid under the given assumptions:

With Assumptions->True, PowerExpand gives general expansion formulas:

Refine and Simplify perform expansions valid under the given assumptions:

Use FunctionExpand to get a different representation of :

Use PiecewiseExpand to represent the result as a piecewise function:

The result given by PowerExpand with Assumptions->Automatic may be incorrect: