Question

Simplify the expression.

Answer 1

`\large\boxed{D.\ 2x^2y\sqrt[5]{7xy^3}}`

Explanation:

`\sqrt[5]{224x^(11)y^8}\\\\=\sqrt[5]{(32)(7)x^(5+5+1)y^(5+3)}\\\\\text{use}\ a^na^m=a^(n+m)\\\\=\sqrt[5]{(2^5)(7)x^5x^5x^1y^5y^3}\\\\\text{use}\ \sqrt[n]{ab}=\sqrt[n]{a}\cdot\sqrt[n]{b}\\\\=\sqrt[5]{2^5}\cdot\sqrt[5]{x^5}\cdot\sqrt[5]{x^5}\cdot\sqrt[5]{y^5}\cdot\sqrt[5]{7xy^3}\\\\\text{use}\ \sqrt[n]{a^n}=a\\\\=2\cdot x\cdot x\cdot y\cdot\sqrt[5]{7xy^3}\\\\=2x^2y\sqrt[5]{7xy^3}`