O.K. You call it a monster

Calculus Level 3

\[ \lim_{x \to a} { \left( \left( \left( \dfrac{a^{1/2}+x^{1/2}}{a^{1/4}-x^{1/4}} \right)^{-1} - \frac{2(ax)^{1/4}}{x^{3/4} - a^{1/4} \times x^{1/2} + a^{1/2} \times x^{1/4}-a^{3/4}} \right)^{-1} –(\sqrt{2})^{\log_{4} {a}} \right)}^{8}\] can be expressed as \(a^{\beta}\) What is the value of \(\beta\)?

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