Question

Solve:

$x^{\sqrt{x}}=\sqrt{x^x}$

Answer 1

$x^{\sqrt{x}}=\sqrt{x^x}$

or, $x^{\sqrt{x}}=x^{\frac{x}{2}}$

or, $\sqrt{x}=\frac{x}{2}$

or, $x-\frac{x^2}{4}=0$

Since $x\ne 0$ then $x=4$.