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\sqrt[3]{\sqrt{4\sqrt{256}}}
Calculate 2 to the power of 8 and get 256.
\sqrt[3]{\sqrt{4\times 16}}
Calculate the square root of 256 and get 16.
\sqrt[3]{\sqrt{64}}
Multiply 4 and 16 to get 64.
\sqrt[3]{8}
Calculate the square root of 64 and get 8.
2
Calculate \sqrt[3]{8} and get 2.