1. **State the problem:** We are given the equation $$Z = \sqrt[3]{\frac{x^2}{w}}$$ and need to make $w$ the subject. 2. **Write the formula and explain:** The cubic root means raising to the power of $\frac{1}{3}$. To isolate $w$, we will first cube both sides to remove the cubic root. 3. **Cube both sides:** $$Z^3 = \left(\sqrt[3]{\frac{x^2}{w}}\right)^3 = \frac{x^2}{w}$$ 4. **Rewrite the equation:** $$Z^3 = \frac{x^2}{w}$$ 5. **Make $w$ the subject by multiplying both sides by $w$:** $$w Z^3 = x^2$$ 6. **Divide both sides by $Z^3$ to isolate $w$:** $$w = \frac{x^2}{Z^3}$$ 7. **Show cancellation step:** $$w = \frac{x^2}{\cancel{Z^3}} \times \frac{\cancel{1}}{1} = \frac{x^2}{Z^3}$$ **Final answer:** $$w = \frac{x^2}{Z^3}$$