Find the sub-triplicate ratio of :

(i) 1 : 216

(ii) $\dfrac{1}{8} : \dfrac{1}{125}$

(iii) 27a³ : 64b³

(i) The sub-triplicate ratio of 1 : 216 is,

$= \sqrt[3]{1} : \sqrt[3]{216} \\[0.5em] = 1 : 6$

Hence, the sub-triplicate ratio is 1 : 6.

(ii) The sub-triplicate ratio of $\dfrac{1}{8} : \dfrac{1}{125}$ is,

$= \sqrt[3]{\dfrac{1}{8}} : \sqrt[3]{\dfrac{1}{125}} \\[0.5em] = \dfrac{1}{2} : \dfrac{1}{5} \\[0.5em] = \dfrac{\dfrac{1}{2}}{\dfrac{1}{5}} \\[0.5em] = \dfrac{5}{2} = 5 : 2$

Hence, the sub-triplicate ratio is 5 : 2.

(iii) The sub-triplicate ratio of 27a³ : 64b³ is,

$= \sqrt[3]{27a^3} : \sqrt[3]{64b^3} \\[0.5em] = 3a : 4b$

Hence, the sub-triplicate ratio is 3a : 4b.