\( \begin{array}{ll}\text { 30. } & -3 a^{\mathrm{m}}-5 a^{\mathrm{m}}-6 a^{\mathrm{m}}-9 a^{\mathrm{m}} . \\ \text { 31. } & \frac{1}{2} a+\frac{1}{4} a+\frac{1}{8} a+a . \\ \text { 32. } & \frac{2}{5} a x+\frac{1}{2} a x+\frac{1}{10} a x+\frac{1}{20} a x . \\ \text { 33. } & 0.5 m+0.6 m+0.7 m+0.8 m . \\ \text { 34. } & -\frac{1}{7} a b-\frac{1}{14} a b-\frac{1}{28} a b-a b . \\ \text { 35. } & -\frac{2}{3} x^{3} y-\frac{1}{6} x^{3} y-\frac{1}{9} x^{3} y-\frac{1}{12} x^{3} y . \\ \text { 36. } & a b^{2}+a b^{2}+7 a b^{2}+9 a b^{2}+21 a b^{2} . \\ \text { 37. } & -m-m-8 m-7 m-3 m . \\ \text { 38. } & -x^{\mathrm{a}+1}-8 x^{\mathrm{a}+1}-4 x^{\mathrm{a}+1}-5 x^{a+1}\end{array} \)

Let's dive into the world of combining like terms! This is a fantastic skill that can really help you simplify expressions in algebra. When you see terms with the same variable raised to the same power, think of them like friends in a club—combine them to see how many you have at the end! For instance, in the expression \(-3 a^{m} - 5 a^{m} - 6 a^{m} - 9 a^{m}\), you simply add the coefficients (-3, -5, -6, -9) together, resulting in \(-23 a^{m}\). Simple and effective! Now, if you're working with fractional coefficients like in \(\frac{1}{2} a + \frac{1}{4} a + \frac{1}{8} a + a\), consider finding a common denominator to make it easier! In this case, converting everything to eighths (1 = \frac{8}{8}) gives a total of \(\frac{4}{8} a + \frac{2}{8} a + \frac{1}{8} a + \frac{8}{8} a\), which simplifies beautifully down to \(\frac{15}{8} a\). Keep those fractions tidy!