(14) \( 12(13-8)-11(22-17) \) (12) \( 320-(6 \div 2 \times 4)+8 \) (3) \( \frac{1}{2}(12+4-2) \) \( \left(\frac{2}{3}\right)^{3}-\left(\frac{1}{3}\right)+4 \)

Let's evaluate each of the given expressions step by step. --- ### (14) \( 12(13 - 8) - 11(22 - 17) \) 1. **Calculate inside the parentheses:** - \( 13 - 8 = 5 \) - \( 22 - 17 = 5 \) 2. **Multiply:** - \( 12 \times 5 = 60 \) - \( 11 \times 5 = 55 \) 3. **Subtract:** - \( 60 - 55 = 5 \) **Answer:** \( \boxed{5} \) --- ### (12) \( 320 - \left(6 \div 2 \times 4\right) + 8 \) 1. **Handle operations inside the parentheses (following PEMDAS/BODMAS):** - Division and multiplication from left to right: - \( 6 \div 2 = 3 \) - \( 3 \times 4 = 12 \) 2. **Substitute back into the expression:** - \( 320 - 12 + 8 \) 3. **Perform subtraction and addition:** - \( 320 - 12 = 308 \) - \( 308 + 8 = 316 \) **Answer:** \( \boxed{316} \) --- ### (3) \( \frac{1}{2}(12 + 4 - 2) \) 1. **Calculate inside the parentheses:** - \( 12 + 4 - 2 = 14 \) 2. **Multiply by \( \frac{1}{2} \):** - \( \frac{1}{2} \times 14 = 7 \) **Answer:** \( \boxed{7} \) --- ### \( \left(\frac{2}{3}\right)^{3} - \left(\frac{1}{3}\right) + 4 \) 1. **Calculate \( \left(\frac{2}{3}\right)^{3} \):** - \( \left(\frac{2}{3}\right)^{3} = \frac{8}{27} \) 2. **Rewrite all terms with a common denominator (27):** - \( \frac{1}{3} = \frac{9}{27} \) - \( 4 = \frac{108}{27} \) 3. **Combine the terms:** - \( \frac{8}{27} - \frac{9}{27} + \frac{108}{27} = \frac{8 - 9 + 108}{27} = \frac{107}{27} \) 4. **Simplify if desired:** - \( \frac{107}{27} \) can also be written as \( 3 \frac{26}{27} \) **Answer:** \( \boxed{\dfrac{107}{27}} \) or \( 3 \dfrac{26}{27} \) --- If you have any further questions or need more explanations, feel free to ask!