Answer:
[tex]\large\boxed{\sqrt[6]{27x^3y^6}=y\sqrt{3x}}[/tex]
Step-by-step explanation:
[tex]\sqrt[6]{27x^3y^6}\qquad\text{use}\ \sqrt[n]{ab}=\sqrt[n]{a}\cdot\sqrt[n]{b}\\\\=\sqrt[6]{3^3}\cdot\sqrt[6]{x^3}\cdot\sqrt[6]{y^6}\qquad\text{use}\ \sqrt[n]{a^m}=a^\frac{m}{n}\\\\=3^\frac{3}{6}\cdot x^\frac{3}{6}\cdot y^\frac{6}{6}\qquad\text{simplify}\\\\=3^\frac{1}{2}\cdot x^\frac{1}{2}\cdot y^1\qquad\text{use}\ (ab)^n=a^n\cdot b^n\\\\=(3x)^\frac{1}{2}\cdot y\\\\=y\sqrt{3x}[/tex]
