The ratio is used for comparing two quantities of the sane kind.
The ratio formula for two numbers says a and b is given by a:b or a/b. When two or more such ratios are equal, they are said to be in proportion.
The concept of ratio and proportion is majorly based on ratios and fractions.
Solution:
Given, $512:216$
${{=}^{3}}\sqrt{512}{{:}^{3}}\sqrt{216}$
$={{\left( {{8}^{3}} \right)}^{1/3}}:{{\left( {{6}^{3}} \right)}^{1/3}}$
$=8:6$
$=8/6$
$=4/3$
$={{\left( {{8}^{3}} \right)}^{1/3}}.{{\left( {{6}^{3}} \right)}^{1/3}}$
$=8:6$
$=8/6$
$=4/3$
Therefore, sub – triplicate ratio is $4:3.$
Solution:
Given, ${{m}^{3}}{{n}^{6}}:{{m}^{6}}{{n}^{3}}$
${{=}^{3}}\sqrt{\left( {{m}^{3}}{{n}^{6}} \right)}{{:}^{3}}\sqrt{\left( {{m}^{6}}n3 \right)}$
$={{\left( {{m}^{3}}{{n}^{6}} \right)}^{1/13}}:{{\left( {{m}^{6}}{{n}^{3}} \right)}^{1/13}}$
$=m{{n}^{2}}:{{m}^{2}}n$
$=m{{n}^{2}}/{{m}^{2}}n$
$=n/m$
Therefore, sub – triplicate ratio is$n:m$