Question

Find the sub-duplicate ratio of the following:
i) $x^6:y^4$

Answer 1

Given: $x^6:y^4$

$x^6:y^4=\frac{x^6}{y^4}$
So, the sub-duplicate ratio of $\frac{x^6}{y^4}$ is,
$\sqrt{\frac{x^6}{y^4}}$
$={\left(\frac{x^6}{y^4}\right)}^{\frac{1}{2}}$

$=\frac{(x{)}^{\frac{6}{2}}}{(y{)}^{\frac{4}{2}}}$

$=\frac{x^3}{y^2}$

Hence, the sub-duplicate ratio of $x^6:y^4\text{is}{x}^3:y^2$.