The expression that is equivalent to the given expression is ![3\sqrt[6]{z}](https://tex.z-dn.net/?f=3%5Csqrt%5B6%5D%7Bz%7D)
<h3>Simplifying an expression</h3>
From the question, we are to determine which of the expressions is equivalent to the given expression
The given expression is
![6\sqrt{z} \div \sqrt[3]{8z}](https://tex.z-dn.net/?f=6%5Csqrt%7Bz%7D%20%20%5Cdiv%20%5Csqrt%5B3%5D%7B8z%7D)
The expression can be simplified as
![6\sqrt{z} \div \sqrt[3]{8z}](https://tex.z-dn.net/?f=6%5Csqrt%7Bz%7D%20%20%5Cdiv%20%5Csqrt%5B3%5D%7B8z%7D)
![\frac{6\sqrt{z}}{\sqrt[3]{8z}}](https://tex.z-dn.net/?f=%5Cfrac%7B6%5Csqrt%7Bz%7D%7D%7B%5Csqrt%5B3%5D%7B8z%7D%7D)
![= \frac{6 \times \sqrt{z}}{\sqrt[3]{8} \times \sqrt[3]{z}}](https://tex.z-dn.net/?f=%3D%20%5Cfrac%7B6%20%5Ctimes%20%5Csqrt%7Bz%7D%7D%7B%5Csqrt%5B3%5D%7B8%7D%20%5Ctimes%20%5Csqrt%5B3%5D%7Bz%7D%7D)



![= 3\times\sqrt[6]{z}](https://tex.z-dn.net/?f=%3D%203%5Ctimes%5Csqrt%5B6%5D%7Bz%7D)
![= 3\sqrt[6]{z}](https://tex.z-dn.net/?f=%3D%203%5Csqrt%5B6%5D%7Bz%7D)
Hence, the expression that is equivalent to the given expression is ![3\sqrt[6]{z}](https://tex.z-dn.net/?f=3%5Csqrt%5B6%5D%7Bz%7D)
Learn more on Simplifying an expression here: brainly.com/question/10864685
#SPJ1