Radical Form Alg 2- I don't need much help, Just a confirmation I'm doing it right

$\sqrt{432}\,=\,\sqrt{2*2*2*2*3*3*3}\,=\,\sqrt{2*2}*\sqrt{2*2}*\sqrt{3*3}*\sqrt3\,=\,2*2*3*\sqrt3$

$=\,12\sqrt3$          Right!

Is this the third one??

$\sqrt[3]{125x^{21}y^{33}}\,\,=\,(125x^{21}y^{33})^{\frac13}\,=\,125^{\frac13}x^{\frac{21}{3}}y^{\frac{33}{3}}\,=\,5x^{7}y^{11}$

$9\sqrt{56x^7y^{12}}\,=\,9\sqrt{2*2*2*7*x*x^6*y^{12}}\,=\,9*\sqrt{2*2}*\sqrt{2*7*x}*\sqrt{x^6}*\sqrt{y^{12}}\\~\\=\,9*2*\sqrt{14x}*x^3*y^6\,=\,18x^3y^6\sqrt{14x}$