Answer:
[tex]\large\boxed{\dfrac{\sqrt{63x^{15}y^9}}{\sqrt{7xy^{11}}}=\dfrac{3\cdot x^7}{y}=\dfrac{3x^7}{y}}[/tex]
Step-by-step explanation:
[tex]\dfrac{\sqrt{63x^{15}y^9}}{\sqrt{7xy^{11}}}\\\\\text{use}\ \sqrt{\dfrac{a}{b}}=\dfrac{\sqrt{a}}{\sqrt{b}}\\\\=\sqrt{\dfrac{63\!\!\!\!\!\diagup^9x^{15}y^9}{7\!\!\!\!\diagup_1xy^{11}}}=\sqrt{\dfrac{9x^{15}y^9}{xy^{11}}}\\\\\text{Cancel x and y respectively}\\\\=\sqrt{\dfrac{9x^{14}}{y^2}}\\\\\text{use}\ \sqrt{\dfrac{a}{b}}=\dfrac{\sqrt{a}}{\sqrt{b}}\ \text{and}\ \sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\\\\=\dfrac{\sqrt9\cdot\sqrt{x^{11}}}{\sqrt{y^2}}\\\\\text{use}\ (a^n)^m=a^{nm}[/tex]
[tex]=\dfrac{\sqrt{3^2}\cdot\sqrt{x^{7\cdot2}}}{\sqrt{y^2}}=\dfrac{\sqrt{3^2}\cdot\sqrt{(x^7)^2}}{\sqrt{y^2}}\\\\\text{use}\ \sqrt{a^2}=a\\\\=\dfrac{3\cdot x^7}{y}=\dfrac{3x^7}{y}[/tex]
