PowerExpand

PowerExpand[expr]

expands all powers of products and powers.

PowerExpand[expr,{x1,x2,}]

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.

Examples

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Basic Examples  (1)

Expand a square root, implicitly assuming positive real values:

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Without PowerExpand, no expansion is done:

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The expansion is only correct for positive real variables:

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This gives a completely correct result:

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This gives a result correct under the specified assumptions:

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Scope  (10)

Generalizations & Extensions  (1)

Options  (3)

Applications  (2)

Properties & Relations  (5)

Possible Issues  (1)

See Also

Expand  Power  Sqrt  Distribute  ComplexExpand  Simplify  FullSimplify  FunctionExpand  Refine

Tutorials

Introduced in 1991
(2.0)
| Updated in 2007
(6.0)