Question

if $x^{x^{\frac{3}{2}}}={\left(x^{\frac{3}{2}}\right)}^2$, then the value of x can be

Answer 1

$x^{x^{\frac{3}{2}}}=(x^{\frac{3}{2}}{)}^2$

$x^{x^{\frac{3}{2}}}=x^{\frac{3}{2}\times 2}=x^3$

$x^{x^{\frac{3}{2}}}=x^3$

Here, the bases are same, so equating the powers

$x^{\frac{3}{2}}=3$

$x=3^{\frac{2}{3}}$.