(a) To find the coefficient of \(\frac{1}{x}\), consider the term \(\binom{5}{2} (2x)^3 \left( \frac{a}{x^2} \right)^2\).

This simplifies to \(10 \times 8x^3 \times \frac{a^2}{x^4} = 720 \times \frac{1}{x}\).

Thus, \(80a^2 = 720\), giving \(a^2 = 9\).

Therefore, \(a = \pm 3\).

(b) To find the coefficient of \(\frac{1}{x^7}\), consider the term \(\binom{5}{4} (2x)^1 \left( \frac{a}{x^2} \right)^4\).

This simplifies to \(5 \times 2x \times \frac{a^4}{x^8}\).

Using \(a = 3\), the coefficient is \(5 \times 2 \times 81 = 810\).