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Workaround? "Simplify" complicates this expression

Posted 16 days ago
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This gives the simplest answer (True):

Refine[a^b (c^d)^b == a^b c^(d b), 
 b \[Element] Integers && d \[Element] Integers]

This does not:

Simplify[a^b (c^d)^b == a^b c^(d b), 
 b \[Element] Integers && d \[Element] Integers]

My understanding of Refine vs. Simplify comes from this tutorial, which only indicates that Simplify should yield something simpler than Refine:

http://reference.wolfram.com/language/tutorial/UsingAssumptions.html

3 Replies
In[14]:= Simplify[a^b (c^d)^b - a^b c^(d b), b \[Element] Integers && d \[Element] Integers]
Out[14]= 0

In[15]:= $Version
Out[15]= "10.4.1 for Microsoft Windows (64-bit) (April 11, 2016)"
Posted 15 days ago

Thanks. That does get me around the problem.

More generally, I am curious why the algorithm used by Simplify prefers anything besides True, if anyone knows. Is there some reason for Simplify not to conform with its description in the tutorial?

Posted 15 days ago
FullSimplify[a^b (c^d)^b == a^b c^(d b), 
 b \[Element] Integers && d \[Element] Integers]

Gives True as well (all I did was replace Simplify with FullSimplify). Generally I just use FullSimplify. It can take a little longer, but many times gets a better result.

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