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, ${{x}^{6}}:{{y}^{4}}$

$={{\sqrt{x}}^{6}}:{{\sqrt{y}}^{4}}$

$={{\left( {{x}^{6}} \right)}^{1/2}}:{{\left( {{y}^{4}} \right)}^{1/2}}$

$={{x}^{3}}:{{y}^{2}}$

Therefore, sub – duplicate ratio is ${{x}^{3}}:{{y}^{2}}$

Solution:

Given,

$63{{m}^{2}}:28{{n}^{2}}$

$=\sqrt{{{\left( 63m \right)}^{2}}}:{{\sqrt{\left( 28 \right)}}^{2}}$

$=3\sqrt{7}m:2\sqrt{7}n$

$=3m:2n$

Therefore, sub – duplicate ratio is $3m:2n$