Explanation

(b)
Let $\alpha$ and $\alpha^{n}$ be the roots of the equation, then
$\alpha + \alpha^{n} = - \frac{b}{a}$ and $\alpha.\alpha^{n} = \frac{c}{a}\ \ \ \Rightarrow \ \ \alpha^{n + 1} = \frac{c}{a}$
On eliminating $\alpha$, we get
$\left( \frac{c}{a} \right)^{\frac{1}{n + 1}} + \left( \frac{c}{a} \right)^{\frac{1}{n + 1}} = - \frac{b}{a}$
$\Rightarrow a.a^{- \frac{1}{n + 1}}c^{\frac{1}{n + 1}} + a.a^{- \frac{n}{n + 1}}c^{\frac{n}{n + 1}} = - b$
$\Rightarrow \left( a^{n}c \right)^{\frac{1}{n + 1}} + \left( ac^{n} \right)^{\frac{1}{n + 1}} = - b$