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 $3m:2n$