28. \( \frac{25}{19}-\frac{6}{19} \) 29. \( \left(\frac{2}{3}\right)^{3} \) 30. \( \sqrt{\frac{48}{2}}-\sqrt{7 \cdot 3+\frac{39}{13}} \) 31. \( \sqrt{\frac{25}{144}} \) 32. \( \frac{4}{3} \cdot \frac{3}{7} \div \frac{13}{14} \)

Calculate the value by following steps: - step0: Calculate: \(\left(\frac{2}{3}\right)^{3}\) - step1: Use the properties of exponents: \(\frac{2^{3}}{3^{3}}\) - step2: Evaluate the power: \(\frac{8}{3^{3}}\) - step3: Evaluate the power: \(\frac{8}{27}\) Calculate or simplify the expression \( 25/19 - 6/19 \). Calculate the value by following steps: - step0: Calculate: \(\frac{25}{19}-\frac{6}{19}\) - step1: Transform the expression: \(\frac{25-6}{19}\) - step2: Subtract the numbers: \(\frac{19}{19}\) - step3: Reduce the numbers: \(\frac{1}{1}\) - step4: Calculate: \(1\) Calculate or simplify the expression \( (4/3) * (3/7) / (13/14) \). Calculate the value by following steps: - step0: Calculate: \(\frac{\frac{4}{3}\times \frac{3}{7}}{\frac{13}{14}}\) - step1: Multiply the numbers: \(\frac{\frac{4}{7}}{\frac{13}{14}}\) - step2: Multiply by the reciprocal: \(\frac{4}{7}\times \frac{14}{13}\) - step3: Reduce the numbers: \(4\times \frac{2}{13}\) - step4: Multiply: \(\frac{4\times 2}{13}\) - step5: Multiply: \(\frac{8}{13}\) Calculate or simplify the expression \( \sqrt(48/2) - \sqrt(7*3 + 39/13) \). Calculate the value by following steps: - step0: Calculate: \(\sqrt{\frac{48}{2}}-\sqrt{7\times 3+\frac{39}{13}}\) - step1: Divide the terms: \(\sqrt{\frac{48}{2}}-\sqrt{7\times 3+3}\) - step2: Multiply the numbers: \(\sqrt{\frac{48}{2}}-\sqrt{21+3}\) - step3: Divide the terms: \(\sqrt{24}-\sqrt{21+3}\) - step4: Add the numbers: \(\sqrt{24}-\sqrt{24}\) - step5: Subtract the terms: \(0\) Calculate or simplify the expression \( \sqrt(25/144) \). Calculate the value by following steps: - step0: Calculate: \(\sqrt{\frac{25}{144}}\) - step1: Use the properties of radicals: \(\frac{\sqrt{25}}{\sqrt{144}}\) - step2: Simplify the expression: \(\frac{5}{12}\) Here are the detailed solutions for each of the problems: 28. **Calculate \( \frac{25}{19} - \frac{6}{19} \)**: - Since both fractions have the same denominator, we can subtract the numerators directly: \[ \frac{25 - 6}{19} = \frac{19}{19} = 1 \] **Result**: \( 1 \) 29. **Calculate \( \left(\frac{2}{3}\right)^{3} \)**: - To find the cube of a fraction, we cube the numerator and the denominator: \[ \left(\frac{2}{3}\right)^{3} = \frac{2^{3}}{3^{3}} = \frac{8}{27} \] **Result**: \( \frac{8}{27} \) 30. **Calculate \( \sqrt{\frac{48}{2}} - \sqrt{7 \cdot 3 + \frac{39}{13}} \)**: - First, simplify \( \frac{48}{2} \): \[ \sqrt{\frac{48}{2}} = \sqrt{24} \] - Next, simplify \( 7 \cdot 3 + \frac{39}{13} \): \[ 7 \cdot 3 = 21 \quad \text{and} \quad \frac{39}{13} = 3 \quad \Rightarrow \quad 21 + 3 = 24 \] - Now, we have: \[ \sqrt{24} - \sqrt{24} = 0 \] **Result**: \( 0 \) 31. **Calculate \( \sqrt{\frac{25}{144}} \)**: - To find the square root of a fraction, we take the square root of the numerator and the denominator: \[ \sqrt{\frac{25}{144}} = \frac{\sqrt{25}}{\sqrt{144}} = \frac{5}{12} \] **Result**: \( \frac{5}{12} \) 32. **Calculate \( \frac{4}{3} \cdot \frac{3}{7} \div \frac{13}{14} \)**: - First, convert the division into multiplication by the reciprocal: \[ \frac{4}{3} \cdot \frac{3}{7} \cdot \frac{14}{13} \] - Now, multiply the fractions: \[ = \frac{4 \cdot 3 \cdot 14}{3 \cdot 7 \cdot 13} \] - The \( 3 \) in the numerator and denominator cancels out: \[ = \frac{4 \cdot 14}{7 \cdot 13} = \frac{56}{91} \] - Simplifying \( \frac{56}{91} \) gives: \[ = \frac{8}{13} \] **Result**: \( \frac{8}{13} \) In summary, the results are: - 28: \( 1 \) - 29: \( \frac{8}{27} \) - 30: \( 0 \) - 31: \( \frac{5}{12} \) - 32: \( \frac{8}{13} \)