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Explicação passo-a-passo:

[tex]a) \sqrt[4]{ \sqrt{20 {}^{20} } } = \sqrt[4 \times 2]{20 {}^{20} } = \sqrt[8]{20 {}^{20} } = \sqrt{20 {}^{5} } = \sqrt{(2 {}^{2} .5) {}^{5} } = \sqrt{2 {}^{10}.5 {}^{5} } = \sqrt{2 {}^{10} .5 {}^{4} .5} = 2 {}^{5} .5 {}^{2} \sqrt{5} = 32.25 \sqrt{5} = 800 \sqrt{5} [/tex]

[tex]b) \sqrt[5]{ \sqrt{ \sqrt[4]{4096} } } = \sqrt[5.2.4]{2 {}^{12} } = \sqrt[40]{2 {}^{12} } = \sqrt[10]{2 {}^{3} } = \sqrt[10]{8} [/tex]

[tex]c) \sqrt[2]{ \sqrt[5]{ \sqrt{3 {}^{4} } } } = \sqrt[2.5.2]{3 {}^{4} } = \sqrt[10]{2 {}^{4} } = \sqrt[5]{2 {}^{2} } = \sqrt[5]{4} [/tex]