This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.

# PowerExpand

 PowerExpand[expr]expands all powers of products and powers. PowerExpandexpands only with respect to the variables .
• PowerExpand also converts to , whatever the form of is.
• The transformations made by PowerExpand are correct in general only if is an integer or and are positive real numbers.
• PowerExpand in general disregards all issues of branches of multivalued functions, so may not preserve the numerical values of expressions.
• PowerExpand automatically threads over lists, as well as equations, inequalities and logic functions.
• The default setting for the Assumptions option is Automatic, corresponding to a maximal set of assumptions.
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 square root, implicitly assuming positive real values:
 Out[1]=
Without PowerExpand, no expansion is done:
 Out[2]=
The expansion is only correct for positive real variables:
 Out[3]=
This gives a completely correct result:
 Out[4]=
This gives a result correct under the specified assumptions:
 Out[5]=
 Scope   (10)
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 and :
 Options   (3)
With the default setting Assumptions the expansions are not always correct:
When the assumptions are specified the result is correct under the given assumptions:
With Assumptions->True, PowerExpand gives a universally correct expansion formula:
 Applications   (2)
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 may be incorrect: