If $y=\frac{a+bx}{c+dx}$  where a, b, c, d are constants and $\lambda y_1{y}_3=\mu y_2^2$ then  ${\mu }^{{\lambda }^2}$=_______ 

$(where \lambda ,\mu are coprime)$

$y=\frac{a+bx}{c+dx}$

$y_1=\frac{bc-ad}{{\left(c+dx\right)}^2},y_2=\frac{\left(bc-ad\right)\left(-2d\right)}{{\left(c+dx\right)}^3},y_3=\frac{\left(bc-ad\right)\left(-2\right)\left(-3\right)d^2}{{\left(c+dx\right)}^4}$

${y_2}^2=\frac{{\left(bc-ad\right)}^{2}4d^2}{{\left(c+dx\right)}^6},y_1{y}_3=\frac{{\left(bc-ad\right)}^{2}6d^2}{{\left(c+dx\right)}^6}$

$\frac{y_1{y}_3}{{y_2}^2}=\frac{3}{2}\Rightarrow \lambda =2,\mu =3$