1. **State the problem:** Simplify the expression $3p^3 \cdot 3p^2$. 2. **Recall the multiplication rules for exponents:** When multiplying terms with the same base, multiply the coefficients and add the exponents: $$a^m \cdot a^n = a^{m+n}$$ 3. **Apply the rule to the coefficients:** Multiply the numbers 3 and 3: $$3 \cdot 3 = 9$$ 4. **Apply the rule to the variables:** Add the exponents of $p$: $$p^3 \cdot p^2 = p^{3+2} = p^5$$ 5. **Combine the results:** $$3p^3 \cdot 3p^2 = 9p^5$$ 6. **Final answer:** $$\boxed{9p^5}$$