1. **State the problem:** We need to determine which expressions equal 80 when $w=4$. 2. **Evaluate each expression:** A) $(5w)^2 = (5 \times 4)^2 = 20^2 = 400$ (not 80) B) $10w^2 = 10 \times 4^2 = 10 \times 16 = 160$ (not 80) C) $w^3 + w^2 = 4^3 + 4^2 = 64 + 16 = 80$ (equals 80) D) $(2w)^2 + 4w = (2 \times 4)^2 + 4 \times 4 = 8^2 + 16 = 64 + 16 = 80$ (equals 80) E) $\frac{w^3}{4} \times 5 = \frac{4^3}{4} \times 5 = \frac{64}{4} \times 5 = 16 \times 5 = 80$ (equals 80) 3. **Conclusion:** Expressions C, D, and E equal 80 when $w=4$. **Final answer:** C,D,E