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Answer 1

The expression that is equivalent to the given expression is $3\sqrt[6]{z}$

Simplifying an expression

From the question, we are to determine which of the expressions is equivalent to the given expression

The given expression is

$6\sqrt{z} \div \sqrt[3]{8z}$

The expression can be simplified as

$6\sqrt{z} \div \sqrt[3]{8z}$

$\frac{6\sqrt{z}}{\sqrt[3]{8z}}$

$= \frac{6 \times \sqrt{z}}{\sqrt[3]{8} \times \sqrt[3]{z}}$

$= \frac{6 \times z^{\frac{1}{2} } }{2 \times z^{\frac{1}{3} }}$

$= 3\times z^{\frac{1}{2} -\frac{1}{3}}$

$= 3\times z^{\frac{1}{6}}$

$= 3\times\sqrt[6]{z}$

$= 3\sqrt[6]{z}$

Hence, the expression that is equivalent to the given expression is $3\sqrt[6]{z}$

Learn more on Simplifying an expression here: brainly.com/question/10864685

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