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\sqrt[3]{\frac{1}{8}}-\sqrt[4]{\sqrt[3]{4096}}
Calculate \sqrt[4]{\frac{1}{4096}} and get \frac{1}{8}.
\frac{1}{2}-\sqrt[4]{\sqrt[3]{4096}}
Calculate \sqrt[3]{\frac{1}{8}} and get \frac{1}{2}.
\frac{1}{2}-\sqrt[4]{16}
Calculate \sqrt[3]{4096} and get 16.
\frac{1}{2}-2
Calculate \sqrt[4]{16} and get 2.
-\frac{3}{2}
Subtract 2 from \frac{1}{2} to get -\frac{3}{2}.