Question: Simplify the expression $$\frac{-3(j^{-3}a^{4})^{-3}}{3j^{4}a^{8}}$$ to its simplest form using only positive exponents.
1. **State the problem:** Simplify $$\frac{-3(j^{-3}a^{4})^{-3}}{3j^{4}a^{8}}$$ so that all exponents are positive.
2. **Recall the exponent rules:**
- When raising a power to another power, multiply the exponents: $$(x^{m})^{n} = x^{mn}$$
- Negative exponents mean reciprocal: $$x^{-m} = \frac{1}{x^{m}}$$
- When dividing like bases, subtract exponents: $$\frac{x^{a}}{x^{b}} = x^{a-b}$$
3. **Simplify the numerator:**
$$-3(j^{-3}a^{4})^{-3} = -3 \times j^{-3 \times (-3)} \times a^{4 \times (-3)} = -3j^{9}a^{-12}$$
4. **Rewrite the original expression:**
$$\frac{-3j^{9}a^{-12}}{3j^{4}a^{8}}$$
5. **Divide coefficients:**
$$\frac{-3}{3} = -1$$
6. **Divide powers with the same base by subtracting exponents:**
$$j^{9} \div j^{4} = j^{9-4} = j^{5}$$
$$a^{-12} \div a^{8} = a^{-12-8} = a^{-20}$$
7. **Combine all parts:**
$$-1 \times j^{5} \times a^{-20} = -j^{5}a^{-20}$$
8. **Rewrite with positive exponents only:**
$$-j^{5}a^{-20} = -\frac{j^{5}}{a^{20}}$$
**Final answer:**
$$\boxed{-\frac{j^{5}}{a^{20}}}$$