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Which expression is equivalent to StartRoot 128 x Superscript 8 Baseline y cubed z Superscript 9 Baseline EndRoot? Assume y greater-than-or-equal-to 0 and z greater-than-or-equal-to 1 2 x squared z squared StartRoot 8 y cubed z EndRoot 4 x squared y z cubed StartRoot 2 x squared EndRoot 8 x Superscript 4 Baseline y z Superscript 4 Baseline StartRoot 2 y z EndRoot 64 x Superscript 4 Baseline y z Superscript 4 Baseline StartRoot 2 y z EndRoot

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Answer:

Option C.

Step-by-step explanation:

The given expression is  

[tex]\sqrt{128x^8y^3z^9}[/tex]

It can be written as

[tex]\sqrt{(64\cdot 2)\cdot x^8\cdot y^{2+1}\cdot z^{8+1}}[/tex]

[tex]=\sqrt{8^2\cdot 2\cdot (x^4)^2\cdot y^{2}\cdot y\cdot (z^{4})^2\cdot z}[/tex]

[tex]=\sqrt{(8x^4yz^4)^2\cdot 2yz}[/tex]

[tex]=8x^4yz^4\sqrt{2yz}[/tex]

Therefore, the correct option is C.

Answer:

c

Step-by-step explanation:

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