If x = a 3 ab a 3 ab ..... , then the value of x is:

Answer: Option D

$$\begin{array}{rl}& x=\sqrt{a\text{root}3\text{of}ab\sqrt{a\text{root}3\text{of}ab}}.....\propto \\ & \text{Square both side}\\ & x^2=a\text{root}3\text{of}abx\left(\because \sqrt{a\text{root}3\text{of}ab}.....\propto \right)\\ & \text{Again cube both sides}\\ & x^6=a^{3}abx\\ & x^5=a^{4}b\\ & x=\text{root}5\text{of}{a}^{4}b\end{array}$$