Evaluate \( \sqrt[3]{343}+\frac{3}{4} \sqrt[3]{-8} \) \( 8 \frac{1}{2} \) \( -5 \frac{1}{2} \) \( -\frac{1}{2} \)

Round the number by following steps: - step0: Round the number to the nearest whole number: \(8.5\) - step1: Round the number to the nearest whole number: \(9\) Round the number \( -5.5 \) into whole number. Round the number by following steps: - step0: Round the number to the nearest whole number: \(-5.5\) - step1: Round the number to the nearest whole number: \(-6\) Round the number \( -0.5 \) into whole number. Round the number by following steps: - step0: Round the number to the nearest whole number: \(-0.5\) - step1: Round the number to the nearest whole number: \(-1\) Calculate or simplify the expression \( \sqrt[3]{343} + \frac{3}{4} \sqrt[3]{-8} \). Calculate the value by following steps: - step0: Calculate: \(\sqrt[3]{343}+\frac{3}{4}\sqrt[3]{-8}\) - step1: Simplify the root: \(7+\frac{3}{4}\sqrt[3]{-8}\) - step2: Simplify the root: \(7+\frac{3}{4}\left(-2\right)\) - step3: Multiply the numbers: \(7-\frac{3}{2}\) - step4: Reduce fractions to a common denominator: \(\frac{7\times 2}{2}-\frac{3}{2}\) - step5: Transform the expression: \(\frac{7\times 2-3}{2}\) - step6: Multiply the numbers: \(\frac{14-3}{2}\) - step7: Subtract the numbers: \(\frac{11}{2}\) Let's evaluate the expression step by step: 1. **Calculate \( \sqrt[3]{343} \)**: - The cube root of \( 343 \) is \( 7 \) because \( 7^3 = 343 \). 2. **Calculate \( \sqrt[3]{-8} \)**: - The cube root of \( -8 \) is \( -2 \) because \( (-2)^3 = -8 \). 3. **Combine the results**: - Now substitute these values into the expression: \[ \sqrt[3]{343} + \frac{3}{4} \sqrt[3]{-8} = 7 + \frac{3}{4} \times (-2) \] - Calculate \( \frac{3}{4} \times (-2) = -\frac{3}{2} \). 4. **Final calculation**: \[ 7 - \frac{3}{2} = 7 - 1.5 = 5.5 \] Thus, the value of the expression \( \sqrt[3]{343} + \frac{3}{4} \sqrt[3]{-8} \) is \( 5.5 \), which can also be expressed as \( 5 \frac{1}{2} \) or \( \frac{11}{2} \). Now, let's summarize the other values: - \( 8 \frac{1}{2} \) rounds to \( 9 \). - \( -5 \frac{1}{2} \) rounds to \( -6 \). - \( -\frac{1}{2} \) rounds to \( -1 \). In conclusion, the evaluated expression is \( 5.5 \) or \( 5 \frac{1}{2} \).