1. **State the problem:** Given the formula $$P_m = \frac{1}{p \times \sqrt[3]{p^2}}$$, find the value of $m$ in terms of $p$. 2. **Rewrite the expression:** The denominator is $p \times \sqrt[3]{p^2}$. Recall that $\sqrt[3]{p^2} = p^{\frac{2}{3}}$. 3. **Combine the powers of $p$ in the denominator:** $$p \times p^{\frac{2}{3}} = p^{1 + \frac{2}{3}} = p^{\frac{3}{3} + \frac{2}{3}} = p^{\frac{5}{3}}$$ 4. **Rewrite $P_m$ using this simplification:** $$P_m = \frac{1}{p^{\frac{5}{3}}}$$ 5. **Express $P_m$ as a power of $p$:** $$P_m = p^{-\frac{5}{3}}$$ 6. **Identify $m$:** Since $P_m = p^m$, we have $$m = -\frac{5}{3}$$ **Final answer:** $$m = -\frac{5}{3}$$