1. **State the problem:** Simplify the expression $$\frac{3}{8}(2^4) + \frac{25}{24}(2^3) - \frac{1}{2}(2)$$. 2. **Recall the powers of 2:** $$2^4 = 16$$ $$2^3 = 8$$ 3. **Substitute these values into the expression:** $$\frac{3}{8} \times 16 + \frac{25}{24} \times 8 - \frac{1}{2} \times 2$$ 4. **Multiply the fractions by the numbers:** $$\frac{3 \times 16}{8} + \frac{25 \times 8}{24} - \frac{1 \times 2}{2}$$ 5. **Simplify each term:** - For the first term: $$\frac{3 \times 16}{8} = \frac{48}{8} = 6$$ - For the second term: $$\frac{25 \times 8}{24} = \frac{200}{24}$$ Simplify by dividing numerator and denominator by 8: $$\frac{\cancel{200}^{25} \times 8}{\cancel{24}^{3} \times 8} = \frac{25}{3}$$ - For the third term: $$\frac{1 \times 2}{2} = \frac{2}{2} = 1$$ 6. **Rewrite the expression with simplified terms:** $$6 + \frac{25}{3} - 1$$ 7. **Combine like terms:** $$6 - 1 = 5$$ So the expression becomes: $$5 + \frac{25}{3}$$ 8. **Convert 5 to a fraction with denominator 3:** $$5 = \frac{15}{3}$$ 9. **Add the fractions:** $$\frac{15}{3} + \frac{25}{3} = \frac{15 + 25}{3} = \frac{40}{3}$$ **Final answer:** $$\frac{40}{3}$$