1. **State the problem:** Simplify the expression $$\frac{3n^4}{2n^{-3}}$$. 2. **Recall the rules:** - When dividing powers with the same base, subtract the exponents: $$a^m \div a^n = a^{m-n}$$. - Negative exponents mean reciprocal: $$a^{-n} = \frac{1}{a^n}$$. 3. **Apply the rules:** $$\frac{3n^4}{2n^{-3}} = \frac{3}{2} \times \frac{n^4}{n^{-3}} = \frac{3}{2} \times n^{4 - (-3)} = \frac{3}{2} \times n^{4 + 3} = \frac{3}{2} n^7$$ 4. **Final answer:** $$\boxed{\frac{3}{2} n^7}$$