1. **State the problem:** Simplify the expression $$\left(\frac{1}{3}\right)^{-3} - \left(\frac{1}{3}\right)^{-4}$$. 2. **Recall the rule for negative exponents:** For any nonzero number $a$ and integer $n$, $$a^{-n} = \frac{1}{a^n}$$. 3. **Apply the rule to each term:** $$\left(\frac{1}{3}\right)^{-3} = 3^3 = 27$$ $$\left(\frac{1}{3}\right)^{-4} = 3^4 = 81$$ 4. **Substitute back into the expression:** $$27 - 81$$ 5. **Calculate the difference:** $$27 - 81 = -54$$ **Final answer:** $$-54$$