Answer:
The correct answer option is [tex] = 8 x ^ 4 y z ^ 4 \sqrt{2yz}[/tex].
Step-by-step explanation:
We are given the following expression and we are to simplify it and determine whether which of the given expressions is equivalent to it, assuming [tex]y\geq 0[/tex] and [tex]z\geq 0[/tex]:
[tex] \sqrt { 128 x ^ 8 y ^ 3 z ^ 9 } [/tex]
Breaking the terms to get:
[tex] \sqrt { 128 x ^ 8 y ^ 3 z ^ 9 } [/tex][tex]=8\sqrt{2yz} \times x^{8\times\frac{1}{2} } \times y^{2\times \frac{1}{2} } \times z^{8\times \frac{1}{2} }[/tex]
[tex] = 8 x ^ 4 y z ^ 4 \sqrt{2yz}[/tex]
