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\sqrt[3]{\frac{1}{9\times 3}}
Express \frac{\frac{1}{9}}{3} as a single fraction.
\sqrt[3]{\frac{1}{27}}
Multiply 9 and 3 to get 27.
\frac{1}{3}
Calculate \sqrt[3]{\frac{1}{27}} and get \frac{1}{3}.