1. The problem is to convert improper fractions into mixed numbers and understand the notation involving roots and powers. 2. For part (a), the fraction is $\frac{27}{4}$. To convert to a mixed number, divide 27 by 4. 3. Perform the division: $27 \div 4 = 6$ remainder $3$. 4. Write the mixed number as $6 \frac{3}{4}$. 5. The notation $4\sqrt{27}$ and $6$ in the problem seems to represent the root and power notation, but the key conversion is the fraction to mixed number. 6. For part (b), the fraction is $\frac{29}{8}$. Divide 29 by 8. 7. Perform the division: $29 \div 8 = 3$ remainder $5$. 8. Write the mixed number as $3 \frac{5}{8}$. 9. The notation $8\sqrt{29}$ and $3$ again relates to root and power notation, but the main focus is the mixed number conversion. Final answers: (a) $\frac{27}{4} = 6 \frac{3}{4}$ (b) $\frac{29}{8} = 3 \frac{5}{8}$