[tex] \sqrt[4]{\dfrac{16x^{11}y^8}{81x^7y^6}}=\sqrt[4]{\dfrac{16}{81}}\cdot\sqrt[4]{\dfrac{x^{11}}{x^7}}\cdot\sqrt[4]{\dfrac{y^8}{y^6}}=\dfrac{\sqrt[4]{16}}{\sqrt[4]{81}}\cdot\sqrt[4]{x^{11-7}}\cdot\sqrt[4]{y^{8-6}}\\\\=\dfrac{2}{3}\cdot\sqrt[4]{x^4}\cdot\sqrt[4]{y^2}=\dfrac{2}{3}\cdot x\cdot y^\frac{2}{4}=\dfrac{2}{3}x\cdot y^\frac{1}{2}=\dfrac{2}{3}x\sqrt{y} [/tex]
[tex] Used:\\\sqrt{a\cdot b}=\sqrt{a}\cdot\sqrt{b}\\\\\dfrac{a^n}{a^m}=a^{n-m}\\\\\sqrt[n]{a^n}=a\\\\\sqrt{\dfrac{a}{b}}=\dfrac{\sqrt{a}}{\sqrt{b}}\\\\\sqrt[n]{a^m}=a^\frac{m}{n} [/tex]
But your answer is:
[tex]...=\dfrac{2}{3}\cdot\sqrt[4]{x^4}\cdot\sqrt[4]{y^2}=\dfrac{2x\left(\sqrt[4]{y^2}\right)}{3}[/tex]
