Упростите выражение: $$\left((a^4 \cdot x^{-0.1})^5 \cdot \sqrt[4]{a^3} \cdot \sqrt{x}\right)^3$$

\(\begin{aligned}\)
&\(\left\)(\(a^4 \cdot x^{-0.1}\)^5 \(\cdot\) \(\sqrt[4]{a^3}\) \(\cdot\) \(\sqrt{x}\)\(\right\))^3 = \(\left\)\(a^{20} \cdot x^{-0.5} \cdot a^{\frac{3}{4}} \cdot x^{\frac{1}{2}}\right\)^3 = \(\left\)\(a^{20+\frac{3}{4}} \cdot x^{-\frac{1}{2}+\frac{1}{2}}\right\)^3 = \(\left\)\(a^{\frac{83}{4}} \cdot x^0\right\)^3 = \(\left\)\(a^{\frac{83}{4}}\right\)^3 = a^{\(\frac{83}{4}\) \(\cdot\) 3} = a^{\(\frac{249}{4}\)}
\(\end{aligned}\)

Ответ: $$a^{\frac{249}{4}}$$