Question

Simplify the following radical

Answer 1

`\large\boxed{2\sqrt[5]{64x^6y}=4x\sqrt[5]{2xy}}`

Explanation:

`\text{Use}\\\sqrt[n]{a^n}=a\\ \sqrt[n]{ab}=\sqrt[n]{a}\cdot\sqrt[n]{b}\\a^n\cdot a^m=a^(nm)\\----------------\\\\2\sqrt[5]{64x^6y}=2\sqrt[5]{64}\cdot\sqrt[5]{x^6}\cdot\sqrt[5]{y}=(*)\\\\\sqrt[5]{64}=\sqrt[5]{32\cdot2}=\sqrt[5]{32}\cdot\sqrt[5]2=\sqrt[5]{2^5}\cdot\sqrt[5]2=2\sqrt[5]2\\\sqrt[5]{x^6}=\sqrt[5]{x^(5+1)}=\sqrt[5]{x^5\cdot x^1}=\sqrt[5]{x^5}\cdot\sqrt[5]{x}=x\sqrt[5]{x}\\\\(*)=2\cdot2\sqrt[5]2\cdot x\sqrt[5]{x}\cdot\sqrt[5]{y}=4x\sqrt[5]{2xy}`