Answer:
[tex](C)8x^4z^4\sqrt{2yz}[/tex]
Step-by-step explanation:
We want to determine an expression equivalent to: [tex]\sqrt{128x^8y^3z^9}[/tex]
[tex]\sqrt{ab} =\sqrt{a}*\sqrt{b}[/tex]
Therefore:
[tex]\sqrt{128x^8y^3z^9}=\sqrt{128}*\sqrt{x^8}*\sqrt{y^3}*\sqrt{z^9}[/tex]
[tex]=\sqrt{64*2}*\sqrt{x^{4*2}}*\sqrt{y^{2+1}}*\sqrt{z^{8+1}}\\=8\sqrt{2}*\sqrt{x^{4*2}}*\sqrt{y^2*y}*\sqrt{z^{8}*z}}[/tex]
[tex]=8\sqrt{2}*x^4*y \sqrt{y}*z^4\sqrt{z}\\=8*x^4*z^4*\sqrt{2}*\sqrt{y}*\sqrt{z}\\=8x^4z^4\sqrt{2yz}[/tex]
