Question

Find the sub-triplicate ratio of the following:
ii) $m^3{n}^6:m^6{n}^3$

Answer 1

Given: $m^3{n}^6:m^6{n}^3$

$\Rightarrow m^3{n}^6:m^6{n}^3=\frac{m^3{n}^6}{m^6{n}^3}$

$\therefore$ Sub-triplicate ratio of $m^3{n}^6:m^6{n}^3$ is,

$\sqrt[3]{3\frac{m^3{n}^6}{m^6{n}^3}}$

$={\left(\frac{n^3}{m^3}\right)}^{\frac{1}{3}}$

$=\frac{(n{)}^{\frac{3}{3}}}{(m{)}^{\frac{3}{3}}}$

$=\frac{n}{m}$

Hence, the sub-triplicate ratio of $m^3{n}^6:m^6{n}^3\text{is}n:m$.