1. **State the problem:** Simplify the expressions $5 \cdot 4^{-1}$ and $9 \cdot 8^{-3}$ using factor form. 2. **Recall the rule for negative exponents:** For any nonzero number $a$ and positive integer $n$, $a^{-n} = \frac{1}{a^n}$. 3. **Simplify $5 \cdot 4^{-1}$:** $$5 \cdot 4^{-1} = 5 \cdot \frac{1}{4} = \frac{5}{4}$$ 4. **Simplify $9 \cdot 8^{-3}$:** First, write $8^{-3}$ as $\frac{1}{8^3}$: $$9 \cdot 8^{-3} = 9 \cdot \frac{1}{8^3} = \frac{9}{8^3}$$ Calculate $8^3$: $$8^3 = 8 \times 8 \times 8 = 512$$ So, $$\frac{9}{512}$$ 5. **Final answers:** - $5 \cdot 4^{-1} = \frac{5}{4}$ - $9 \cdot 8^{-3} = \frac{9}{512}$