# Unexpectedly Powerful

Algebra Level 4

Consider all triples of real numbers $$(x,y,z)$$ such that $$x, y, z \geq \frac{1}{2}$$ and $$x+y+z = 3$$.

If the minimum and maximum values of $$x^x y^y z^ z$$ are $$A$$ and $$B$$, respectively, what is $$A+B$$?

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