Question

Please hurry I’m in desperate need of an explanation and a answer

Answer 1

`\large\boxed{D.\ 4x^2y\sqrt[4]{3y}}`

Explanation:

`\sqrt[4]{768x^8y^5}\\\\\text{Prime factorization of 768:}\\\\\begin{array}c768&2\\384&2\\192&2\\96&2\\48&2\\24&2\\12&2\\6&2\\3&3\\1\end{array}\\\\768=2^8\cdot3\\\\\sqrt[4]{768x^8y^5}=\sqrt[4]{(2^8)(3)x^8y^5}\qquad\text{use}\ a^n\cdot a^m=a^(n+m)\\\\=\sqrt{(2^(4+4))(3)x^(4+4)y^(4+1)}=√((2^4)(2^4)(3)(x^4)(x^4)(y^4)(y))\\\\\text{use}\ \sqrt[n]{ab}=\sqrt[n]{a}\cdot\sqrt[n]{b}`

`=\sqrt[4]{2^4}\cdot\sqrt[4]{2^4}\cdot\sqrt[4]{x^4}\cdot\sqrt[4]{x^4}\cdot\sqrt[4]{y^4}\cdot\sqrt[4]{3y}\qquad\text{use}\ \sqrt[n]{a^n}=a\\\\=2\cdot2\cdot x\cdot x\cdot y\cdot\sqrt[4]{3y}\\\\=4x^2y\sqrt[4]{3y}`