1. **State the problem:** Evaluate the expression $(-4)^5 \cdot 8^4$. 2. **Recall the rules:** - When raising a negative number to an odd power, the result is negative. - Calculate powers separately, then multiply. 3. **Calculate each power:** $$(-4)^5 = (-4) \times (-4) \times (-4) \times (-4) \times (-4)$$ Since 5 is odd, the result is negative. Calculate $4^5$: $$4^5 = 4 \times 4 \times 4 \times 4 \times 4 = 1024$$ So, $$(-4)^5 = -1024$$ Calculate $8^4$: $$8^4 = 8 \times 8 \times 8 \times 8 = 4096$$ 4. **Multiply the results:** $$(-4)^5 \cdot 8^4 = -1024 \times 4096$$ Calculate: $$-1024 \times 4096 = -4194304$$ 5. **Final answer:** $$\boxed{-4194304}$$