1. Problem: Simplify the expression $$\frac{\frac{1}{3}x - 3}{\frac{1}{3}x^{-4}}$$. 2. Formula and rules: To divide by a quantity multiply by its reciprocal, so $$\frac{A}{B}=A\cdot\frac{1}{B}$$. 3. Important rules: Remember $x^{-4}=\frac{1}{x^{4}}$ and when multiplying powers add exponents so $x^{a}x^{b}=x^{a+b}$. 4. Apply the reciprocal: Rewriting the denominator's reciprocal gives $$\frac{1}{\frac{1}{3}x^{-4}}=3x^{4}$$. 5. Multiply the numerator by the reciprocal: $$\left(\frac{1}{3}x-3\right)\cdot 3x^{4}$$. 6. Distribute: $$3x^{4}\cdot\frac{1}{3}x - 3x^{4}\cdot 3$$. 7. Show cancellation of the numeric factor explicitly: $$3x^{4}\cdot\frac{1}{3}x=\left(\cancel{3}\cdot\frac{1}{\cancel{3}}\right)x^{4}x= x^{5}$$. 8. Simplify the second term: $$3x^{4}\cdot 3=9x^{4}$$. 9. Combine results: $$x^{5}-9x^{4}$$. 10. Factor out the common factor $x^{4}$ to get the final simplified form: $$x^{4}(x-9)$$. 11. Final answer: $$x^{4}(x-9)$$.