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\sqrt[3]{\sqrt{\frac{1}{729}}}
Calculate 729 to the power of -1 and get \frac{1}{729}.
\sqrt[3]{\frac{1}{27}}
Rewrite the square root of the division \frac{1}{729} as the division of square roots \frac{\sqrt{1}}{\sqrt{729}}. Take the square root of both numerator and denominator.
\frac{1}{3}
Calculate \sqrt[3]{\frac{1}{27}} and get \frac{1}{3}.