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[tex]\sqrt{a\sqrt[4]{a\sqrt{a} } } = \sqrt{a\sqrt[4]{a*a^{\frac{1}{2} } } } =\sqrt{a\sqrt[4]{a^{\frac{3}{2} } } } =\sqrt{a*a^{\frac{3}{8} } } = \sqrt{a^{\frac{11}{8} } } = a^{\frac{11}{16} }[/tex]