If $${x^{x\sqrt x }} = {\left( {x\sqrt x } \right)^x}{\text{,}}$$    then x equals to?

Solution (By Examveda Team)

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