1. **State the problem:** Simplify the expression $$-8a^{-4}b^{-3}$$ by writing it with positive exponents only and avoiding radicals. 2. **Recall the rule for negative exponents:** For any nonzero variable $x$ and integer $n$, $$x^{-n} = \frac{1}{x^n}$$. This means a negative exponent indicates the reciprocal of the base raised to the positive exponent. 3. **Apply the rule to each term:** - For $a^{-4}$, rewrite as $$\frac{1}{a^4}$$. - For $b^{-3}$, rewrite as $$\frac{1}{b^3}$$. 4. **Rewrite the entire expression:** $$-8a^{-4}b^{-3} = -8 \times \frac{1}{a^4} \times \frac{1}{b^3} = -\frac{8}{a^4 b^3}$$ 5. **Final answer:** $$\boxed{-\frac{8}{a^4 b^3}}$$ This expression has only positive exponents and no radicals, as required.