\( 3 \sqrt{-8} a+3 x(-2)^{2} \) b. \( 24-8 \div 2^{3} \) c. \( -3^{2} \div\left(2+(-1)^{2}\right) \)

Calculate the value by following steps: - step0: Calculate: \(24-\frac{8}{2^{3}}\) - step1: Divide the terms: \(24-1\) - step2: Subtract the numbers: \(23\) Calculate or simplify the expression \( -3^2 / (2 + (-1)^2) \). Calculate the value by following steps: - step0: Calculate: \(-\frac{3^{2}}{\left(2+\left(-1\right)^{2}\right)}\) - step1: Remove the parentheses: \(-\frac{3^{2}}{2+\left(-1\right)^{2}}\) - step2: Evaluate the power: \(-\frac{3^{2}}{2+1}\) - step3: Add the numbers: \(-\frac{3^{2}}{3}\) - step4: Reduce the fraction: \(-3\) Calculate or simplify the expression \( 3 * \sqrt(-8) * a + 3 * x * (-2)^2 \). Simplify the expression by following steps: - step0: Solution: \(3\sqrt{-8}\times a+3x\left(-2\right)^{2}\) - step1: Simplify the root: \(3\times 2\sqrt{2}\times ia+3x\left(-2\right)^{2}\) - step2: Multiply the numbers: \(6\sqrt{2}\times ia+3x\left(-2\right)^{2}\) - step3: Multiply the numbers: \(6\sqrt{2}\times ia+12x\) Here are the simplified results for each expression: a. For the expression \( 3 \sqrt{-8} a + 3 x (-2)^{2} \): - The term \( \sqrt{-8} \) can be simplified to \( 2\sqrt{2}i \) (where \( i \) is the imaginary unit). - The term \( (-2)^{2} \) equals \( 4 \). - Therefore, the expression simplifies to: \[ 3 \cdot 2\sqrt{2}i \cdot a + 3 \cdot x \cdot 4 = 6\sqrt{2}ia + 12x \] b. For the expression \( 24 - 8 \div 2^{3} \): - First, calculate \( 2^{3} = 8 \). - Then, \( 8 \div 8 = 1 \). - Finally, \( 24 - 1 = 23 \). - So, the simplified result is: \[ 23 \] c. For the expression \( -3^{2} \div (2 + (-1)^{2}) \): - First, calculate \( -3^{2} = -9 \). - Then, \( (-1)^{2} = 1 \), so \( 2 + 1 = 3 \). - Finally, \( -9 \div 3 = -3 \). - Thus, the simplified result is: \[ -3 \] In summary: - a: \( 6\sqrt{2}ia + 12x \) - b: \( 23 \) - c: \( -3 \)