If $(a^m)^n = a^{m^n}$,then the value of $m$ in terms of $n$ is

The rationalising factor of $a^{1/3} + a^{-1/3}$ is

If $x = 3 - \sqrt{5}$,then $\frac{\sqrt{x}}{\sqrt{2} + \sqrt{3x - 2}} = $

Let $\frac{7}{2^{1/2} + 2^{1/4} + 1} = A + B \cdot 2^{1/4} + C \cdot 2^{1/2} + D \cdot 2^{3/4}$,where $A, B, C, D$ are rational numbers. Which of the following is true?

If ${\left( \frac{2}{3} \right)^{x + 2}} = {\left( \frac{3}{2} \right)^{2 - 2x}}$,then $x =$

$({x^5})^{1/3} \times (16{x^3})^{2/3} \times \left( \frac{1}{4}{x^{4/9}} \right)^{-3/2} = ?$