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PowerExpand

PowerExpand[expr]
expands all powers of products and powers.
PowerExpand
expands 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:
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Without PowerExpand, no expansion is done:
In[2]:=
Click for copyable input
Out[2]=
The expansion is only correct for positive real variables:
In[3]:=
Click for copyable input
Out[3]=
This gives a completely correct result:
In[4]:=
Click for copyable input
Out[4]=
This gives a result correct under the specified assumptions:
In[5]:=
Click for copyable input
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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 :
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:
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->Automatic may be incorrect:
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