[tex] \sqrt{\dfrac{y^3}{9x^2y^7}}=\sqrt{\dfrac{1}{3^2x^2y^4}}=\sqrt{\dfrac{1}{3^2x^2(y^2)^2}}=\dfrac{\sqrt1}{\sqrt{3^2x^2(y^2)^2}}\\\\=\dfrac{1}{\sqrt{3^3}\cdot\sqrt{x^2}\cdot\sqrt{(y^2)^2}}=\dfrac{1}{3xy^2}\\\\Used:\\\\\sqrt{\dfrac{a}{b}}=\dfrac{\sqrt{a}}{\sqrt{b}}\\\\\sqrt{a\cdot b}=\sqrt{a}\cdot\sqrt{b}\\\\\sqrt{a^2}=a [/tex]
