Question

x^x√x=(x√x)^x then x is

Answer 1

x^x√x = x^(x^3/2)
now (x√x)^x = (x^3/2)^x = x^(3/2×x)
=> x^(x^3/2) = x^(3/2×x)
=> x^3/2 = 3/2×x
=> (x^3/2)/x = 3/2
=> x^(3/2 - 1) = 3/2
=> x^(1/2) = 3/2
now squaring both sides
=> x = (3/2)^2 = 9/4

Answer 2

Given  x^{x √x} = (x √x)^x

Take Logarithm on both sides and apply:   Log yⁿ = n Log y.

      {x √x} * Log x  = x Log (x √x)
          x³/²  * Log x = x Log ( x³/² )
          x¹/²  * Log x  = Log x³/²
                              = 3/2 * Log x

      =>  x¹/² = 3/2
            x = (3/2)² = 9/4