1. **State the problem:** Simplify the expression $$\frac{(2c^6)(4c)}{8c^3}$$ and express the answer with positive exponents. 2. **Write the expression:** $$\frac{(2c^6)(4c)}{8c^3}$$ 3. **Multiply the numerator terms:** Multiply the coefficients and add exponents of like bases. $$2 \times 4 = 8$$ $$c^6 \times c^1 = c^{6+1} = c^7$$ So numerator becomes $$8c^7$$. 4. **Rewrite the expression:** $$\frac{8c^7}{8c^3}$$ 5. **Cancel common factors:** $$\frac{\cancel{8}c^7}{\cancel{8}c^3} = \frac{c^7}{c^3}$$ 6. **Simplify the powers of c:** Subtract exponents when dividing like bases. $$c^{7-3} = c^4$$ 7. **Final answer:** $$c^4$$ The expression simplifies to $$c^4$$ with positive exponents.