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Simplify:square root of cube root of 512\(((512)^\frac13)^\frac12\) |
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Answer» \(\begin{array}{c|c}2 & 512 \\ \hline 2 & 256 \\ \hline 2&128\\\hline 2&64\\\hline2&32\\\hline 2&16\\\hline 2& 8\\\hline 2&4\\\hline 2&2\\\hline&1 \end{array}\) \(((512)^\frac13)^\frac12\) \( = ((2^9)^\frac13)^\frac12\) \(= (2^3)^\frac12\) \(= 8^\frac12\) \(= (4 \times 2)^\frac12\) \(= 2\sqrt2\) |
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