33. \( 3\left(\sqrt{\frac{144}{81}}\right) \) 34. \( \left(\frac{4}{9}\right)^{3} \div 8 \)

Calculate the value by following steps: - step0: Calculate: \(\frac{\left(\frac{4}{9}\right)^{3}}{8}\) - step1: Simplify the expression: \(\frac{\frac{4^{3}}{9^{3}}}{8}\) - step2: Rewrite the expression: \(\frac{4^{3}}{5832}\) - step3: Evaluate the power: \(\frac{64}{5832}\) - step4: Reduce the fraction: \(\frac{8}{729}\) Calculate or simplify the expression \( 3*\sqrt(144/81) \). Calculate the value by following steps: - step0: Calculate: \(3\sqrt{\frac{144}{81}}\) - step1: Reduce the fraction: \(3\sqrt{\frac{16}{9}}\) - step2: Simplify the root: \(3\times \frac{4}{3}\) - step3: Reduce the numbers: \(1\times 4\) - step4: Simplify: \(4\) Let's solve the two expressions step by step. ### Problem 33: \( 3\left(\sqrt{\frac{144}{81}}\right) \) 1. **Calculate the fraction inside the square root:** \[ \frac{144}{81} = \frac{144 \div 9}{81 \div 9} = \frac{16}{9} \] 2. **Take the square root:** \[ \sqrt{\frac{16}{9}} = \frac{\sqrt{16}}{\sqrt{9}} = \frac{4}{3} \] 3. **Multiply by 3:** \[ 3 \left(\frac{4}{3}\right) = 4 \] Thus, the result for Problem 33 is \( 4 \). --- ### Problem 34: \( \left(\frac{4}{9}\right)^{3} \div 8 \) 1. **Calculate \( \left(\frac{4}{9}\right)^{3} \):** \[ \left(\frac{4}{9}\right)^{3} = \frac{4^3}{9^3} = \frac{64}{729} \] 2. **Divide by 8:** \[ \frac{64}{729} \div 8 = \frac{64}{729} \times \frac{1}{8} = \frac{64}{729 \times 8} = \frac{64}{5832} \] 3. **Simplify the fraction:** \[ \frac{64}{5832} = \frac{8}{729} \quad (\text{after dividing both numerator and denominator by 8}) \] Alternatively, in decimal form, this is approximately \( 0.010974 \). Thus, the result for Problem 34 is \( \frac{8}{729} \) or approximately \( 0.010974 \).