Question

`\sqrt[6]{27x^(3)y^(6) }`

Answer 1

`\large\boxed{\sqrt[6]{27x^3y^6}=y√(3x)}`

Explanation:

`\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^(m)/(n)\\\\=3^(3)/(6)\cdot x^(3)/(6)\cdot y^(6)/(6)\qquad\text{simplify}\\\\=3^(1)/(2)\cdot x^(1)/(2)\cdot y^1\qquad\text{use}\ (ab)^n=a^n\cdot b^n\\\\=(3x)^(1)/(2)\cdot y\\\\=y√(3x)`