If x^x x = ( x x )^x , then x equals to?

Answer: Option C

$$\begin{array}{rl}& x^{x\sqrt{x}}={\left(x\sqrt{x}\right)}^x\\ & x^{x\sqrt{x}}={\left(x^{\frac{3}{2}}\right)}^x\\ & x^{x\sqrt{x}}=x^{\frac{3}{2}x}\end{array}$$
(If bases are same then their power is also same)
$$\begin{array}{rl}& \therefore x\sqrt{x}=\frac{3}{2}x\\ & \Rightarrow \sqrt{x}=\frac{3}{2}\\ & \Rightarrow x={\left(\frac{3}{2}\right)}^2\\ & \Rightarrow x=\frac{9}{4}\end{array}$$