Suppose that \(y^3\) varies inversely with \(\sqrt[3]{z}\). If y=2 when z=1, find the value of z when y=4. Express your answer in simplest fractional form.
+37158 y^3 = k/(cubrt(z))
2^3 = k /(cubrt(1) results in
k = 8
y^3 = 8/(cubrt(z))
When y = 4 find z
4^3 = 8 /(cubrt z)
8/4^3 = cubrt z
8 / 64 = cubrt z
1/8 = cubrt z cube both sides of the equation to find 'z'
1 / 512 = z When y = 4
