a. \( \left(-\frac{8}{3}\right)^{2}+\sqrt[3]{-\frac{1}{729}} \cdot \frac{11}{3}+\left(-\frac{4}{3}\right)^{3}= \) f. \( \left(\frac{7}{5}-\frac{7}{10}\right)^{2}-\frac{3}{5} \cdot \sqrt{-\frac{36}{25}+\frac{8}{5}}= \) b. \( \frac{36}{5}:\left(-\frac{5}{8}\right)^{-1}+\sqrt{\frac{27}{16}-\frac{1}{8}}-\frac{13}{4}= \) g. \( \sqrt{\left(\frac{6}{5}+\frac{16}{3}\right) \cdot\left(\frac{35}{6}-\frac{5}{2}\right)}-\frac{4}{9}:\left(\frac{4}{9}\right)^{2}= \) c. \( \sqrt[3]{\frac{13}{5}+\frac{18}{125}}:\left(-\frac{49}{25}\right)+\left(-\frac{5}{4}+\frac{2}{3}\right)^{-1}= \) h. \( \frac{18}{11} \cdot\left(\frac{3}{4}-\frac{5}{3}\right)^{2}+\sqrt{\left(\frac{5}{6}+\frac{5}{4}\right):\left(\frac{27}{5}-\frac{1}{15}\right)}= \) d. \( \left(-\frac{5}{3}\right):\left(-\frac{1}{2}\right)^{2}+\left(-\frac{18}{7}\right) \cdot \frac{35}{9}+\sqrt[4]{\frac{625}{81}}= \) i. \( \sqrt[3]{\frac{18}{21}} \cdot \sqrt[3]{-\frac{36}{49}}-\left(-\frac{1}{4}-\frac{1}{5}+\frac{1}{20}\right)^{-1}= \) e. \( \sqrt{\frac{8}{11} \cdot \frac{18}{11}}+\left(\frac{7}{5}-\frac{9}{10}\right)^{2}+\frac{3}{44}= \) j. \( \frac{8}{3} \cdot\left(\frac{4}{3}+2\right)^{-1}-\sqrt[3]{\frac{135}{32}}: \sqrt[3]{\frac{5}{4}}= \)

Calculate the value by following steps: - step0: Calculate: \(\left(\frac{-8}{3}\right)^{2}+\left(\frac{-1}{729}\right)^{\frac{1}{3}}\times \frac{11}{3}+\left(\frac{-4}{3}\right)^{3}\) - step1: Rewrite the fraction: \(\left(\frac{-8}{3}\right)^{2}+\left(-\frac{1}{729}\right)^{\frac{1}{3}}\times \frac{11}{3}+\left(\frac{-4}{3}\right)^{3}\) - step2: Rewrite the fraction: \(\left(-\frac{8}{3}\right)^{2}+\left(-\frac{1}{729}\right)^{\frac{1}{3}}\times \frac{11}{3}+\left(\frac{-4}{3}\right)^{3}\) - step3: Rewrite the fraction: \(\left(-\frac{8}{3}\right)^{2}+\left(-\frac{1}{729}\right)^{\frac{1}{3}}\times \frac{11}{3}+\left(-\frac{4}{3}\right)^{3}\) - step4: Multiply the numbers: \(\left(-\frac{8}{3}\right)^{2}-\frac{11}{27}+\left(-\frac{4}{3}\right)^{3}\) - step5: Evaluate the power: \(\frac{64}{9}-\frac{11}{27}+\left(-\frac{4}{3}\right)^{3}\) - step6: Evaluate the power: \(\frac{64}{9}-\frac{11}{27}-\frac{64}{27}\) - step7: Reduce fractions to a common denominator: \(\frac{64\times 3}{9\times 3}-\frac{11}{27}-\frac{64}{27}\) - step8: Multiply the numbers: \(\frac{64\times 3}{27}-\frac{11}{27}-\frac{64}{27}\) - step9: Transform the expression: \(\frac{64\times 3-11-64}{27}\) - step10: Multiply the numbers: \(\frac{192-11-64}{27}\) - step11: Subtract the numbers: \(\frac{117}{27}\) - step12: Reduce the fraction: \(\frac{13}{3}\) Calculate or simplify the expression \( (7/5 - 7/10)^2 - (3/5) * \sqrt(-36/25 + 8/5) \). Calculate the value by following steps: - step0: Calculate: \(\left(\frac{7}{5}-\frac{7}{10}\right)^{2}-\frac{3}{5}\sqrt{\frac{-36}{25}+\frac{8}{5}}\) - step1: Subtract the numbers: \(\left(\frac{7}{10}\right)^{2}-\frac{3}{5}\sqrt{\frac{-36}{25}+\frac{8}{5}}\) - step2: Rewrite the fraction: \(\left(\frac{7}{10}\right)^{2}-\frac{3}{5}\sqrt{-\frac{36}{25}+\frac{8}{5}}\) - step3: Add the numbers: \(\left(\frac{7}{10}\right)^{2}-\frac{3}{5}\sqrt{\frac{4}{25}}\) - step4: Simplify the root: \(\left(\frac{7}{10}\right)^{2}-\frac{3}{5}\times \frac{2}{5}\) - step5: Multiply the numbers: \(\left(\frac{7}{10}\right)^{2}-\frac{6}{25}\) - step6: Simplify: \(\frac{7^{2}}{10^{2}}-\frac{6}{25}\) - step7: Evaluate the power: \(\frac{49}{100}-\frac{6}{25}\) - step8: Reduce fractions to a common denominator: \(\frac{49}{100}-\frac{6\times 4}{25\times 4}\) - step9: Multiply the numbers: \(\frac{49}{100}-\frac{6\times 4}{100}\) - step10: Transform the expression: \(\frac{49-6\times 4}{100}\) - step11: Multiply the numbers: \(\frac{49-24}{100}\) - step12: Subtract the numbers: \(\frac{25}{100}\) - step13: Reduce the fraction: \(\frac{1}{4}\) Calculate or simplify the expression \( (-5/3) / (-1/2)^2 + (-18/7) * (35/9) + (625/81)^(1/4) \). Calculate the value by following steps: - step0: Calculate: \(\frac{\left(\frac{-5}{3}\right)}{\left(\frac{-1}{2}\right)^{2}}+\left(\frac{-18}{7}\right)\times \frac{35}{9}+\left(\frac{625}{81}\right)^{\frac{1}{4}}\) - step1: Remove the parentheses: \(\frac{\frac{-5}{3}}{\left(\frac{-1}{2}\right)^{2}}+\left(\frac{-18}{7}\right)\times \frac{35}{9}+\left(\frac{625}{81}\right)^{\frac{1}{4}}\) - step2: Rewrite the fraction: \(\frac{\frac{-5}{3}}{\left(-\frac{1}{2}\right)^{2}}+\left(\frac{-18}{7}\right)\times \frac{35}{9}+\left(\frac{625}{81}\right)^{\frac{1}{4}}\) - step3: Rewrite the fraction: \(\frac{\frac{-5}{3}}{\left(-\frac{1}{2}\right)^{2}}+\left(-\frac{18}{7}\right)\times \frac{35}{9}+\left(\frac{625}{81}\right)^{\frac{1}{4}}\) - step4: Remove the parentheses: \(\frac{\frac{-5}{3}}{\left(-\frac{1}{2}\right)^{2}}-\frac{18}{7}\times \frac{35}{9}+\left(\frac{625}{81}\right)^{\frac{1}{4}}\) - step5: Rewrite the fraction: \(\frac{-\frac{5}{3}}{\left(-\frac{1}{2}\right)^{2}}-\frac{18}{7}\times \frac{35}{9}+\left(\frac{625}{81}\right)^{\frac{1}{4}}\) - step6: Divide the terms: \(-\frac{20}{3}-\frac{18}{7}\times \frac{35}{9}+\left(\frac{625}{81}\right)^{\frac{1}{4}}\) - step7: Multiply the numbers: \(-\frac{20}{3}-10+\left(\frac{625}{81}\right)^{\frac{1}{4}}\) - step8: Evaluate the power: \(-\frac{20}{3}-10+\frac{5}{3}\) - step9: Reduce fractions to a common denominator: \(-\frac{20}{3}-\frac{10\times 3}{3}+\frac{5}{3}\) - step10: Transform the expression: \(\frac{-20-10\times 3+5}{3}\) - step11: Multiply the numbers: \(\frac{-20-30+5}{3}\) - step12: Calculate: \(\frac{-45}{3}\) - step13: Reduce the numbers: \(\frac{-15}{1}\) - step14: Calculate: \(-15\) Calculate or simplify the expression \( \sqrt(8/11 * 18/11) + (7/5 - 9/10)^2 + 3/44 \). Calculate the value by following steps: - step0: Calculate: \(\sqrt{\frac{\frac{8}{11}\times 18}{11}}+\left(\frac{7}{5}-\frac{9}{10}\right)^{2}+\frac{3}{44}\) - step1: Subtract the numbers: \(\sqrt{\frac{\frac{8}{11}\times 18}{11}}+\left(\frac{1}{2}\right)^{2}+\frac{3}{44}\) - step2: Multiply the numbers: \(\sqrt{\frac{\frac{144}{11}}{11}}+\left(\frac{1}{2}\right)^{2}+\frac{3}{44}\) - step3: Divide the terms: \(\sqrt{\frac{144}{121}}+\left(\frac{1}{2}\right)^{2}+\frac{3}{44}\) - step4: Simplify the root: \(\frac{12}{11}+\left(\frac{1}{2}\right)^{2}+\frac{3}{44}\) - step5: Evaluate the power: \(\frac{12}{11}+\frac{1}{4}+\frac{3}{44}\) - step6: Reduce fractions to a common denominator: \(\frac{12\times 4}{11\times 4}+\frac{11}{4\times 11}+\frac{3}{44}\) - step7: Multiply the numbers: \(\frac{12\times 4}{44}+\frac{11}{4\times 11}+\frac{3}{44}\) - step8: Multiply the numbers: \(\frac{12\times 4}{44}+\frac{11}{44}+\frac{3}{44}\) - step9: Transform the expression: \(\frac{12\times 4+11+3}{44}\) - step10: Multiply the numbers: \(\frac{48+11+3}{44}\) - step11: Add the numbers: \(\frac{62}{44}\) - step12: Reduce the fraction: \(\frac{31}{22}\) Calculate or simplify the expression \( (8/3) * (4/3 + 2)^-1 - (135/32)^(1/3) / (5/4)^(1/3) \). Calculate the value by following steps: - step0: Calculate: \(\frac{8}{3}\left(\frac{4}{3}+2\right)-1-\frac{\left(\frac{135}{32}\right)^{\frac{1}{3}}}{\left(\frac{5}{4}\right)^{\frac{1}{3}}}\) - step1: Add the numbers: \(\frac{8}{3}\times \frac{10}{3}-1-\frac{\left(\frac{135}{32}\right)^{\frac{1}{3}}}{\left(\frac{5}{4}\right)^{\frac{1}{3}}}\) - step2: Divide the terms: \(\frac{8}{3}\times \frac{10}{3}-1-\frac{27^{\frac{1}{3}}}{8^{\frac{1}{3}}}\) - step3: Multiply the numbers: \(\frac{80}{9}-1-\frac{27^{\frac{1}{3}}}{8^{\frac{1}{3}}}\) - step4: Evaluate the power: \(\frac{80}{9}-1-\frac{3}{2}\) - step5: Reduce fractions to a common denominator: \(\frac{80\times 2}{9\times 2}-\frac{9\times 2}{9\times 2}-\frac{3\times 9}{2\times 9}\) - step6: Multiply the numbers: \(\frac{80\times 2}{18}-\frac{9\times 2}{9\times 2}-\frac{3\times 9}{2\times 9}\) - step7: Multiply the numbers: \(\frac{80\times 2}{18}-\frac{9\times 2}{18}-\frac{3\times 9}{2\times 9}\) - step8: Multiply the numbers: \(\frac{80\times 2}{18}-\frac{9\times 2}{18}-\frac{3\times 9}{18}\) - step9: Transform the expression: \(\frac{80\times 2-9\times 2-3\times 9}{18}\) - step10: Multiply the numbers: \(\frac{160-9\times 2-3\times 9}{18}\) - step11: Multiply the numbers: \(\frac{160-18-3\times 9}{18}\) - step12: Multiply the numbers: \(\frac{160-18-27}{18}\) - step13: Subtract the numbers: \(\frac{115}{18}\) Calculate or simplify the expression \( (13/5 + 18/125)^(1/3) / (-49/25) + (-5/4 + 2/3)^-1 \). Calculate the value by following steps: - step0: Calculate: \(\frac{\left(\frac{13}{5}+\frac{18}{125}\right)^{\frac{1}{3}}}{\left(\frac{-49}{25}\right)}+\left(\frac{-5}{4}+\frac{2}{3}\right)-1\) - step1: Remove the parentheses: \(\frac{\left(\frac{13}{5}+\frac{18}{125}\right)^{\frac{1}{3}}}{\frac{-49}{25}}+\left(\frac{-5}{4}+\frac{2}{3}\right)-1\) - step2: Add the numbers: \(\frac{\left(\frac{343}{125}\right)^{\frac{1}{3}}}{\frac{-49}{25}}+\left(\frac{-5}{4}+\frac{2}{3}\right)-1\) - step3: Rewrite the fraction: \(\frac{\left(\frac{343}{125}\right)^{\frac{1}{3}}}{\frac{-49}{25}}+\left(-\frac{5}{4}+\frac{2}{3}\right)-1\) - step4: Add the numbers: \(\frac{\left(\frac{343}{125}\right)^{\frac{1}{3}}}{\frac{-49}{25}}+\left(-\frac{7}{12}\right)-1\) - step5: Remove the parentheses: \(\frac{\left(\frac{343}{125}\right)^{\frac{1}{3}}}{\frac{-49}{25}}-\frac{7}{12}-1\) - step6: Rewrite the fraction: \(\frac{\left(\frac{343}{125}\right)^{\frac{1}{3}}}{-\frac{49}{25}}-\frac{7}{12}-1\) - step7: Divide the terms: \(-\frac{5}{7}-\frac{7}{12}-1\) - step8: Reduce fractions to a common denominator: \(-\frac{5\times 12}{7\times 12}-\frac{7\times 7}{12\times 7}-\frac{7\times 12}{7\times 12}\) - step9: Multiply the numbers: \(-\frac{5\times 12}{84}-\frac{7\times 7}{12\times 7}-\frac{7\times 12}{7\times 12}\) - step10: Multiply the numbers: \(-\frac{5\times 12}{84}-\frac{7\times 7}{84}-\frac{7\times 12}{7\times 12}\) - step11: Multiply the numbers: \(-\frac{5\times 12}{84}-\frac{7\times 7}{84}-\frac{7\times 12}{84}\) - step12: Transform the expression: \(\frac{-5\times 12-7\times 7-7\times 12}{84}\) - step13: Multiply the numbers: \(\frac{-60-7\times 7-7\times 12}{84}\) - step14: Multiply the numbers: \(\frac{-60-49-7\times 12}{84}\) - step15: Multiply the numbers: \(\frac{-60-49-84}{84}\) - step16: Subtract the numbers: \(\frac{-193}{84}\) - step17: Rewrite the fraction: \(-\frac{193}{84}\) Calculate or simplify the expression \( (36/5) / ((-5/8)^-1) + \sqrt(27/16 - 1/8) - 13/4 \). Calculate the value by following steps: - step0: Calculate: \(\frac{\frac{36}{5}}{\left(\left(\frac{-5}{8}\right)-1\right)}+\sqrt{\frac{27}{16}-\frac{1}{8}}-\frac{13}{4}\) - step1: Remove the parentheses: \(\frac{\frac{36}{5}}{\left(\frac{-5}{8}\right)-1}+\sqrt{\frac{27}{16}-\frac{1}{8}}-\frac{13}{4}\) - step2: Rewrite the fraction: \(\frac{\frac{36}{5}}{\left(-\frac{5}{8}\right)-1}+\sqrt{\frac{27}{16}-\frac{1}{8}}-\frac{13}{4}\) - step3: Remove the parentheses: \(\frac{\frac{36}{5}}{-\frac{5}{8}-1}+\sqrt{\frac{27}{16}-\frac{1}{8}}-\frac{13}{4}\) - step4: Subtract the numbers: \(\frac{\frac{36}{5}}{-\frac{13}{8}}+\sqrt{\frac{27}{16}-\frac{1}{8}}-\frac{13}{4}\) - step5: Subtract the numbers: \(\frac{\frac{36}{5}}{-\frac{13}{8}}+\sqrt{\frac{25}{16}}-\frac{13}{4}\) - step6: Divide the terms: \(-\frac{288}{65}+\sqrt{\frac{25}{16}}-\frac{13}{4}\) - step7: Simplify the root: \(-\frac{288}{65}+\frac{5}{4}-\frac{13}{4}\) - step8: Reduce fractions to a common denominator: \(-\frac{288\times 4}{65\times 4}+\frac{5\times 65}{4\times 65}-\frac{13\times 65}{4\times 65}\) - step9: Multiply the numbers: \(-\frac{288\times 4}{260}+\frac{5\times 65}{4\times 65}-\frac{13\times 65}{4\times 65}\) - step10: Multiply the numbers: \(-\frac{288\times 4}{260}+\frac{5\times 65}{260}-\frac{13\times 65}{4\times 65}\) - step11: Multiply the numbers: \(-\frac{288\times 4}{260}+\frac{5\times 65}{260}-\frac{13\times 65}{260}\) - step12: Transform the expression: \(\frac{-288\times 4+5\times 65-13\times 65}{260}\) - step13: Multiply the numbers: \(\frac{-1152+5\times 65-13\times 65}{260}\) - step14: Multiply the numbers: \(\frac{-1152+325-13\times 65}{260}\) - step15: Multiply the numbers: \(\frac{-1152+325-845}{260}\) - step16: Calculate: \(\frac{-1672}{260}\) - step17: Reduce the fraction: \(\frac{-418}{65}\) - step18: Rewrite the fraction: \(-\frac{418}{65}\) Calculate or simplify the expression \( \sqrt((6/5 + 16/3) * (35/6 - 5/2)) - (4/9) / (4/9)^2 \). Calculate the value by following steps: - step0: Calculate: \(\sqrt{\left(\frac{6}{5}+\frac{16}{3}\right)\left(\frac{35}{6}-\frac{5}{2}\right)}-\frac{\frac{4}{9}}{\left(\frac{4}{9}\right)^{2}}\) - step1: Add the numbers: \(\sqrt{\frac{98}{15}\left(\frac{35}{6}-\frac{5}{2}\right)}-\frac{\frac{4}{9}}{\left(\frac{4}{9}\right)^{2}}\) - step2: Subtract the numbers: \(\sqrt{\frac{98}{15}\times \frac{10}{3}}-\frac{\frac{4}{9}}{\left(\frac{4}{9}\right)^{2}}\) - step3: Multiply the numbers: \(\sqrt{\frac{196}{9}}-\frac{\frac{4}{9}}{\left(\frac{4}{9}\right)^{2}}\) - step4: Simplify the root: \(\frac{14}{3}-\frac{\frac{4}{9}}{\left(\frac{4}{9}\right)^{2}}\) - step5: Divide the terms: \(\frac{14}{3}-\frac{9}{4}\) - step6: Reduce fractions to a common denominator: \(\frac{14\times 4}{3\times 4}-\frac{9\times 3}{4\times 3}\) - step7: Multiply the numbers: \(\frac{14\times 4}{12}-\frac{9\times 3}{4\times 3}\) - step8: Multiply the numbers: \(\frac{14\times 4}{12}-\frac{9\times 3}{12}\) - step9: Transform the expression: \(\frac{14\times 4-9\times 3}{12}\) - step10: Multiply the numbers: \(\frac{56-9\times 3}{12}\) - step11: Multiply the numbers: \(\frac{56-27}{12}\) - step12: Subtract the numbers: \(\frac{29}{12}\) Calculate or simplify the expression \( (18/21)^(1/3) * (-36/49)^(1/3) - (-1/4 - 1/5 + 1/20)^-1 \). Calculate the value by following steps: - step0: Calculate: \(\left(\frac{18}{21}\right)^{\frac{1}{3}}\left(\frac{-36}{49}\right)^{\frac{1}{3}}-\left(\frac{-1}{4}-\frac{1}{5}+\frac{1}{20}\right)-1\) - step1: Reduce the fraction: \(\left(\frac{6}{7}\right)^{\frac{1}{3}}\left(\frac{-36}{49}\right)^{\frac{1}{3}}-\left(\frac{-1}{4}-\frac{1}{5}+\frac{1}{20}\right)-1\) - step2: Rewrite the fraction: \(\left(\frac{6}{7}\right)^{\frac{1}{3}}\left(-\frac{36}{49}\right)^{\frac{1}{3}}-\left(\frac{-1}{4}-\frac{1}{5}+\frac{1}{20}\right)-1\) - step3: Rewrite the fraction: \(\left(\frac{6}{7}\right)^{\frac{1}{3}}\left(-\frac{36}{49}\right)^{\frac{1}{3}}-\left(-\frac{1}{4}-\frac{1}{5}+\frac{1}{20}\right)-1\) - step4: Calculate: \(\left(\frac{6}{7}\right)^{\frac{1}{3}}\left(-\frac{36}{49}\right)^{\frac{1}{3}}-\left(-\frac{2}{5}\right)-1\) - step5: Remove the parentheses: \(\left(\frac{6}{7}\right)^{\frac{1}{3}}\left(-\frac{36}{49}\right)^{\frac{1}{3}}+\frac{2}{5}-1\) - step6: Multiply the numbers: \(-\left(\frac{216}{343}\right)^{\frac{1}{3}}+\frac{2}{5}-1\) - step7: Evaluate the power: \(-\frac{6}{7}+\frac{2}{5}-1\) - step8: Reduce fractions to a common denominator: \(-\frac{6\times 5}{7\times 5}+\frac{2\times 7}{5\times 7}-\frac{7\times 5}{7\times 5}\) - step9: Multiply the numbers: \(-\frac{6\times 5}{35}+\frac{2\times 7}{5\times 7}-\frac{7\times 5}{7\times 5}\) - step10: Multiply the numbers: \(-\frac{6\times 5}{35}+\frac{2\times 7}{35}-\frac{7\times 5}{7\times 5}\) - step11: Multiply the numbers: \(-\frac{6\times 5}{35}+\frac{2\times 7}{35}-\frac{7\times 5}{35}\) - step12: Transform the expression: \(\frac{-6\times 5+2\times 7-7\times 5}{35}\) - step13: Multiply the numbers: \(\frac{-30+2\times 7-7\times 5}{35}\) - step14: Multiply the numbers: \(\frac{-30+14-7\times 5}{35}\) - step15: Multiply the numbers: \(\frac{-30+14-35}{35}\) - step16: Calculate: \(\frac{-51}{35}\) - step17: Rewrite the fraction: \(-\frac{51}{35}\) Calculate or simplify the expression \( (18/11) * (3/4 - 5/3)^2 + \sqrt((5/6 + 5/4) / (27/5 - 1/15)) \). Calculate the value by following steps: - step0: Calculate: \(\frac{18}{11}\left(\frac{3}{4}-\frac{5}{3}\right)^{2}+\sqrt{\frac{\left(\frac{5}{6}+\frac{5}{4}\right)}{\left(\frac{27}{5}-\frac{1}{15}\right)}}\) - step1: Remove the parentheses: \(\frac{18}{11}\left(\frac{3}{4}-\frac{5}{3}\right)^{2}+\sqrt{\frac{\frac{5}{6}+\frac{5}{4}}{\frac{27}{5}-\frac{1}{15}}}\) - step2: Subtract the numbers: \(\frac{18}{11}\left(-\frac{11}{12}\right)^{2}+\sqrt{\frac{\frac{5}{6}+\frac{5}{4}}{\frac{27}{5}-\frac{1}{15}}}\) - step3: Add the numbers: \(\frac{18}{11}\left(-\frac{11}{12}\right)^{2}+\sqrt{\frac{\frac{25}{12}}{\frac{27}{5}-\frac{1}{15}}}\) - step4: Subtract the numbers: \(\frac{18}{11}\left(-\frac{11}{12}\right)^{2}+\sqrt{\frac{\frac{25}{12}}{\frac{16}{3}}}\) - step5: Divide the terms: \(\frac{18}{11}\left(-\frac{11}{12}\right)^{2}+\sqrt{\frac{25}{64}}\) - step6: Simplify the root: \(\frac{18}{11}\left(-\frac{11}{12}\right)^{2}+\frac{5}{8}\) - step7: Multiply the numbers: \(\frac{11}{2^{3}}+\frac{5}{8}\) - step8: Evaluate the power: \(\frac{11}{8}+\frac{5}{8}\) - step9: Transform the expression: \(\frac{11+5}{8}\) - step10: Add the numbers: \(\frac{16}{8}\) - step11: Reduce the numbers: \(\frac{2}{1}\) - step12: Calculate: \(2\) Aquí están las soluciones a los problemas matemáticos que proporcionaste: a. \[ \left(-\frac{8}{3}\right)^{2}+\sqrt[3]{-\frac{1}{729}} \cdot \frac{11}{3}+\left(-\frac{4}{3}\right)^{3} = \frac{13}{3} \quad \text{o} \quad 4\frac{1}{3} \quad \text{o} \quad 4.\dot{3} \] b. \[ \frac{36}{5}:\left(-\frac{5}{8}\right)^{-1}+\sqrt{\frac{27}{16}-\frac{1}{8}}-\frac{13}{4} = -\frac{418}{65} \quad \text{o} \quad -6\frac{28}{65} \quad \text{o} \quad -6.4\dot{3}0769\dot{2} \] c. \[ \sqrt[3]{\frac{13}{5}+\frac{18}{125}}:\left(-\frac{49}{25}\right)+\left(-\frac{5}{4}+\frac{2}{3}\right)^{-1} = -\frac{193}{84} \quad \text{o} \quad -2\frac{25}{84} \quad \text{o} \quad -2.29\dot{7}6190\dot{4} \] d. \[ \left(-\frac{5}{3}\right):\left(-\frac{1}{2}\right)^{2}+\left(-\frac{18}{7}\right) \cdot \frac{35}{9}+\sqrt[4]{\frac{625}{81}} = 2 \quad \text{o} \quad 2.0 \] e. \[ \sqrt{\frac{8}{11} \cdot \frac{18}{11}}+\left(\frac{7}{5}-\frac{9}{10}\right)^{2}+\frac{3}{44} = \frac{31}{22} \quad \text{o} \quad 1\frac{9}{22} \quad \text{o} \quad 1.4\dot{0}\dot{9} \] f. \[ \left(\frac{7}{5}-\frac{7}{10}\right)^{2}-\frac{3}{5} \cdot \sqrt{-\frac{36}{25}+\frac{8}{5}} = 2 \] g. \[ \sqrt{\left(\frac{6}{5}+\frac{16}{3}\right) \cdot\left(\frac{35}{6}-\frac{5}{2}\right)}-\frac{4}{9}:\left(\frac{4}{9}\right)^{2} = -\frac{51}{35} \quad \text{o} \quad -1\frac{16}{35} \quad \text{o} \quad -1.4\dot{5}7142\dot{8} \] h. \[ \frac{18}{11} \cdot\left(\frac{3}{4}-\frac{5}{3}\right)^{2}+\sqrt{\left(\frac{5}{6}+\frac{5}{4}\right):\left(\frac{27}{5}-\frac{1}{15}\right)} = \frac{115}{18} \quad \text{o} \quad 6\frac{7}{18} \quad \text{o} \quad 6.3\dot{8} \] i. \[ \sqrt[3]{\frac{18}{21}} \cdot \sqrt[3]{-\frac{36}{49}}-\left(-\frac{1}{4}-\frac{1}{5}+\frac{1}{20}\right)^{-1} = -15 \] j. \[ \frac{8}{3} \cdot\left(\frac{4}{3}+2\right)^{-1}-\sqrt[3]{\frac{135}{32}}: \sqrt[3]{\frac{5}{4}} = \frac{115}{18} \quad \text{o} \quad 6\frac{7}{18} \quad \text{o} \quad 6.3\dot{8} \] Si necesitas más detalles sobre algún cálculo específico, házmelo saber.