Simplify: $\sqrt[3]{\frac{125}{343}}$

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Solution

$\sqrt[3]{\frac{125}{343}}$

$= \sqrt[3]{\frac{5 \times 5 \times 5}{7 \times 7 \times 7}}$

$= \sqrt[3]{\frac{5^{3}}{7^{3}}}$

$= \sqrt[3]{{(\frac{5}{7})}^{3}}$

$= \frac{5}{7}$

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Find the value of $\sqrt[3]{343}$ + $\sqrt[3]{\frac{512}{125}}$

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