PowerExpand

PowerExpand[expr]
expands all powers of products and powers.

PowerExpand[expr, {x1, x2, ...}]
expands only with respect to the variables .

Details and OptionsDetails 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.

ExamplesExamplesopen allclose all

Basic Examples (1)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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