Write an equation describing the relationship of the given variables.
$y$ varies inversely as the cube root of $x$ and when $x=8, y=2$.

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Answer

Write the final equation with the value of $k$: $\boxed{y = 4 * \frac{1}{\sqrt[3]{x}}}$

Steps

Step 1 ：Write an equation describing the relationship of the given variables: $y = k * \frac{1}{\sqrt[3]{x}}$

Step 2 ：Use the given values $x=8$ and $y=2$ to find the value of $k$: $2 = k * \frac{1}{\sqrt[3]{8}}$

Step 3 ：Solve for $k$: $k = 4$

Step 4 ：Write the final equation with the value of $k$: $\boxed{y = 4 * \frac{1}{\sqrt[3]{x}}}$