Sure! Here is the explanation written using MathJax:

If x varies inversely as the cube root of y, then the product of x and the cube root of y is a constant. Let's denote this constant as k. Then, we can write the relationship between x and y as:

\(x y^{\frac{1}{3}} = k\)

Since x = 1 when y = 8, we can substitute these values into the equation to find the value of k:

\(1 8^{\frac{1}{3}} = k\)

\(k = 2\)

Now that we know the value of k, we can use the equation to find the value of y when x = 3:

\(3 y^{\frac{1}{3}} = 2\)

\(y^{\frac{1}{3}} = \frac{2}{3}\)

\(y = (\frac{2}{3})^3 = \frac{8}{27}\)

Therefore, when x = 3, the value of y is \(\frac{8}{27}\).