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PowerExpand

  • PowerExpand[ expr ] expands all powers of products and powers.
  • Example: PowerExpand[Sqrt[x y]].
  • PowerExpand converts ( a b )^ c to a ^ c b ^ c, whatever the form of c is.
  • PowerExpand also converts ( a ^ b )^ c to a ^( b c ), whatever the form of c is.
  • The transformations made by PowerExpand are correct in general only if c is an integer or a and b are positive real numbers.
  • PowerExpand converts Log[ a ^ b ] to b Log[ a ].
  • See the Mathematica book: Section 1.4.5Section 3.3.1.
  • See also: Expand, Distribute, ComplexExpand, FullSimplify.

    Further Examples

    Mathematica does not expand powers into products since the "law of powers" is not valid for all possible values of a and b.

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    PowerExpand does such expansions with no guarantee that the resulting expression is mathematically equivalent to the original expression for all values of the variables.

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