29. \( \frac{1}{16 a}+\frac{5}{12 b}-\frac{9}{10 b^{3}} \)

Calculate or simplify the expression \( \frac{1}{16a}+\frac{5}{12b}-\frac{9}{10b^{3}} \). Simplify the expression by following steps: - step0: Solution: \(\frac{1}{16a}+\frac{5}{12b}-\frac{9}{10b^{3}}\) - step1: Reduce fractions to a common denominator: \(\frac{3\times 5b\times b^{2}}{16a\times 3\times 5b\times b^{2}}+\frac{5\times 4\times 5ab^{2}}{12b\times 4\times 5ab^{2}}-\frac{9\times 6\times 4a}{10b^{3}\times 6\times 4a}\) - step2: Multiply the terms: \(\frac{3\times 5b\times b^{2}}{240ab\times b^{2}}+\frac{5\times 4\times 5ab^{2}}{12b\times 4\times 5ab^{2}}-\frac{9\times 6\times 4a}{10b^{3}\times 6\times 4a}\) - step3: Multiply the terms: \(\frac{3\times 5b\times b^{2}}{240ab\times b^{2}}+\frac{5\times 4\times 5ab^{2}}{240bab^{2}}-\frac{9\times 6\times 4a}{10b^{3}\times 6\times 4a}\) - step4: Multiply the terms: \(\frac{3\times 5b\times b^{2}}{240ab\times b^{2}}+\frac{5\times 4\times 5ab^{2}}{240bab^{2}}-\frac{9\times 6\times 4a}{240b^{3}a}\) - step5: Multiply: \(\frac{3\times 5b\times b^{2}}{240ab^{3}}+\frac{5\times 4\times 5ab^{2}}{240bab^{2}}-\frac{9\times 6\times 4a}{240b^{3}a}\) - step6: Multiply: \(\frac{3\times 5b\times b^{2}}{240ab^{3}}+\frac{5\times 4\times 5ab^{2}}{240b^{3}a}-\frac{9\times 6\times 4a}{240b^{3}a}\) - step7: Rewrite the expression: \(\frac{3\times 5b\times b^{2}}{240ab^{3}}+\frac{5\times 4\times 5ab^{2}}{240ab^{3}}-\frac{9\times 6\times 4a}{240ab^{3}}\) - step8: Transform the expression: \(\frac{3\times 5b\times b^{2}+5\times 4\times 5ab^{2}-9\times 6\times 4a}{240ab^{3}}\) - step9: Multiply the terms: \(\frac{15b^{3}+5\times 4\times 5ab^{2}-9\times 6\times 4a}{240ab^{3}}\) - step10: Multiply the terms: \(\frac{15b^{3}+100ab^{2}-9\times 6\times 4a}{240ab^{3}}\) - step11: Multiply the terms: \(\frac{15b^{3}+100ab^{2}-216a}{240ab^{3}}\) The simplified form of the expression \( \frac{1}{16a}+\frac{5}{12b}-\frac{9}{10b^{3}} \) is \( \frac{15b^{3}+100ab^{2}-216a}{240ab^{3}} \).