1. **State the problem:** Simplify the expression $$\frac{w^3}{w^{-3}}$$. 2. **Recall the rule for division of exponents with the same base:** When dividing powers with the same base, subtract the exponents: $$\frac{a^m}{a^n} = a^{m-n}$$. 3. **Apply the rule:** $$\frac{w^3}{w^{-3}} = w^{3 - (-3)}$$ 4. **Simplify the exponent:** $$3 - (-3) = 3 + 3 = 6$$ 5. **Final simplified expression:** $$w^6$$ So, $$\frac{w^3}{w^{-3}} = w^6$$.