Step-by-step Solution:

To expand the expression \( E = \frac{(9 + 2x)^{1/2}(3 + 4x)}{(1 - x)^{1/5}} \) and simplify it by neglecting higher powers of \( x \), we can proceed with the following steps: 1. Rewrite the Expression: \[ E = (9 + 2x)^{1/2}(3 + 4x)(1 - x)^{-1/5} \] 2. Factor Out Constants: \[ E = \left[ 3\left(1 + \frac{2}{9}x\right)^{1/2} \right] \left[ 3\left(1 + \frac{4}{3}x\right) \right] (1 - x)^{-1/5} \] 3. Expand Each Term Using Binomial Expansion (Neglecting Higher Powers): \[ (1 + \frac{2}{9}x)^{1/2} \approx 1 + \frac{1}{2} \cdot \frac{2}{9}x = 1 + \frac{1}{9}x \] \[ (1 + \frac{4}{3}x) \approx 1 + \frac{4}{3}x \] \[ (1 - x)^{-1/5} \approx 1 + \frac{1}{5}x \] 4. Multiply the Expanded Terms: \[ E = 9 \left(1 + \frac{1}{9}x\right) \left(1 + \frac{4}{3}x\right) \left(1 + \frac{1}{5}x\right) \] Neglecting higher powers of \( x \): \[ E \approx 9 \left(1 + \frac{1}{9}x + \frac{4}{3}x\right) \left(1 + \frac{1}{5}x\right) \] \[ E \approx 9 \left(1 + \frac{13}{9}x\right) \left(1 + \frac{1}{5}x\right) \] \[ E \approx 9 \left(1 + \frac{13}{9}x + \frac{1}{5}x\right) \] \[ E \approx 9 \left(1 + \frac{74}{45}x\right) \] 5. Final Simplification: \[ E \approx 9 + \frac{74}{5}x \] Therefore, the expanded and simplified form of \( E \) is: \[ \boxed{9 + \frac{74}{5}x} \]