Irrational numbers raised to irrational powers

Use the laws of exponents to evaluate \sqrt{2}^{\sqrt{2}^{\sqrt{2}}}.

[Source: Wikipedia. See below.]

a^b = \left(\sqrt{2}^{\sqrt{2}}\right)^{\sqrt{2}} = \sqrt{2}^{\left(\sqrt{2}\cdot\sqrt{2}\right)} = \sqrt{2}^2 = 2,

 

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