The subtriplicate ratio of $64 m^{6} : 27 n^{3}$ is ____

27 n^{3} : 64 m^{6}

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4 m : 3 n

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4 m^{2} : 3 n

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4 m^{3} : 3 n

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Solution

The correct option is D $4 m^{2} : 3 n$
The subtriplicate ratio of $a : b$ is $\sqrt[3]{a} : \sqrt[3]{b}$
$∴$ The subtriplicate ratio of $64 m^{6} : 27 n^{3}$ is $\sqrt[3]{64 m^{6}} : \sqrt[3]{27 n^{3}}$
$= 4 m^{2} : 3 n$

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