expands all powers of products and powers.
expands only with respect to the variables xi.
Details and Options
- PowerExpand converts to , whatever the form of is.
- 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 converts Log[a^b] to bLog[a].
- 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.
- PowerExpand has the option Assumptions, specifying assumptions to use.
- The default setting for the Assumptions option is Automatic, corresponding to a maximal set of assumptions.
- You can specify default assumptions for PowerExpand using Assuming.
Examplesopen allclose all
Basic Examples (1)
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:
With the default setting Assumptions -> Automatic 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:
Properties & Relations (5)
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:
Possible Issues (1)
The result given by PowerExpand with Assumptions->Automatic may be incorrect:
Wolfram Research (1991), PowerExpand, Wolfram Language function, https://reference.wolfram.com/language/ref/PowerExpand.html (updated 2007).
Wolfram Language. 1991. "PowerExpand." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2007. https://reference.wolfram.com/language/ref/PowerExpand.html.
Wolfram Language. (1991). PowerExpand. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/PowerExpand.html