What is \sqrt[a^{a^a}]{(a^a)^{a^a}} ?

The solution to \sqrt[a^{a^a}]{(a^a)^{a^a}} is a^{a^{a-a^a+1}}

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simplify \sqrt[a^{a^a}]{(a^a)^{a^a}}

simplify

a^{a^{a - a^{a} + 1}}

Solution steps

(a^{a})^{a^{a}} : a^{a^{1 + a}}

Apply radical rule:

assuming

a \geq 0

= a^{\frac{a ^{1 + a}}{a ^{a^{a}}}}

\frac{a ^{1 + a}}{a ^{a^{a}}} = a^{1 + a - a^{a}}

= a^{a^{1 + a - a^{a}}}

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What is \sqrt[a^{a^a}]{(a^a)^{a^a}} ?
The solution to \sqrt[a^{a^a}]{(a^a)^{a^a}} is a^{a^{a-a^a+1}}