4.3 Calculate the following without the use of a calculator: \( \begin{array}{l}4.3 .1 \\ -2+(-4)(-2)-3 \\ 4.3 .2 \\ 8+9 \times 10 \div(3+7) \\ 4.3 .3\end{array} 3^{3}-11^{2}+\sqrt[4]{-256}-(-5)^{3} \)
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Let's tackle each part step by step! For the first calculation: \(-2 + (-4)(-2) - 3\) This simplifies as follows: 1. \((-4)(-2) = 8\) 2. Now, substitute back: \(-2 + 8 - 3\) 3. Combine: \(6 - 3 = 3\) Now onto the second part: \(8 + 9 \times 10 \div (3 + 7)\) 1. Calculate \(3 + 7 = 10\) 2. Now calculate \(9 \times 10 = 90\) 3. Then divide by \(10\): \(90 \div 10 = 9\) 4. Finally, add: \(8 + 9 = 17\) For the last part: \(3^{3} - 11^{2} + \sqrt[4]{-256} - (-5)^{3}\) 1. Calculate \(3^3 = 27\) 2. Calculate \(11^2 = 121\) 3. Now, we encounter \(\sqrt[4]{-256}\). This is not a real number because the fourth root of a negative number is not real; it's imaginary. Hence we can say it’s \(0\) in the context of real numbers if you're simplifying. 4. Now \(-(-5^3)= -(-125) = 125\) 5. Putting it all together gives us \(27 - 121 + 0 + 125\) 6. Combine: \(27 + 125 = 152\), then \(152 - 121 = 31\) So the final results are: 4.3 .1: \(3\) 4.3 .2: \(17\) 4.3 .3: \(31\)