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

Sure! To simplify the expression \( \frac{1}{16 a} + \frac{5}{12 b} - \frac{9}{10 b^{3}} \), we need a common denominator. The denominators here are \( 16a \), \( 12b \), and \( 10b^3 \). The least common multiple (LCM) of these denominators would be \( 240ab^3 \). Now, we can rewrite each fraction with the common denominator: 1. \( \frac{1}{16 a} = \frac{15b^3}{240ab^3} \) (multiplied numerator and denominator by \( 15b^3 \)) 2. \( \frac{5}{12 b} = \frac{100ab^2}{240ab^3} \) (multiplied by \( 20ab^2 \)) 3. \( \frac{9}{10 b^{3}} = \frac{216a}{240ab^3} \) (multiplied by \( 24a \)) Now substituting these into the original equation gives: \[ \frac{15b^3 + 100ab^2 - 216a}{240ab^3} \] Thus, the simplified expression is \( \frac{15b^3 + 100ab^2 - 216a}{240ab^3} \).