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bdjinsd1-Visitor
1-Visitor
May 10, 2018
Solved

How to simplify exponents of exponents

When doing symbolic math, sometimes the result has exponents of exponents, for instance

 

(x^2)^(3/2)

 

A simpler form for this expression would be x^3, but even using "simplify,max" does not change the form of the  result. "combine" and "expand" don't help either.

 

Is there any way to get Matchcad to simplify this expression?

 

Werner_E
Werner_EAnswer
25-Diamond I
May 10, 2018

(x^2)^(3/2) = x^3 is true for x>=0 only, not for x<0.

And if x is non-real, the square root ()^.../2 has two results, not just one like x^3.

Mathcad takes that into account and will only simplify to x^3 if you tell it with the "assume" that x is positive (that implicitly also tells MC that x is real of course).

b.png

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2 replies

Werner_E
Werner_E25-Diamond IAnswer
25-Diamond I
May 10, 2018

(x^2)^(3/2) = x^3 is true for x>=0 only, not for x<0.

And if x is non-real, the square root ()^.../2 has two results, not just one like x^3.

Mathcad takes that into account and will only simplify to x^3 if you tell it with the "assume" that x is positive (that implicitly also tells MC that x is real of course).

b.png

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    bdjinsd1-VisitorAuthor
    1-Visitor
    May 11, 2018

    Ah, that helps. Thanks!

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