Упростите выражение ... значение при а=4

Решите задачу:

$\sqrt{\frac{2a}{\left(1+a\right)\cdot\sqrt[3]{1+a}}}\cdot\sqrt[3]{\frac{4+\frac{8}{a}+\frac{4}{a^2}}{\sqrt{2}}}, \ \ \ a=2;\\ \sqrt{\sqrt[3]{\frac{\left(2a\right)^3}{\left(1+a\right)^3\cdot\left(1+a\right)}}}\cdot\sqrt[3]{\sqrt{\frac{\left(4+\frac8a+\frac{4}{a^2}\right)^2}{2}}}=\\ =\sqrt[6]{\frac{\left(2a\right)^3}{\left(1+a\right)^4}\cdot\frac{\left(4+\frac8a+\frac{4}{a^2}\right)^2}{2}}=\\ =\sqrt[6]{\frac{8^3}{5^4}\cdot\frac{\left(4+2+\frac14\right)^2}{2}}=\\$

$=\sqrt[6]{\frac{8^3}{5^4}\cdot\frac{\left(4+2+\frac14\right)^2}{2}}=\\ =\sqrt[6]{\frac{8^3}{5^4}\cdot\frac{\frac{25^2}{4^2}}{2}} =\\ =\sqrt[6]{\frac{2^9}{5^4}\cdot\frac{5^4}{2^5}}=\\ =\sqrt[6]{\frac{2^9}{2^5}}=\sqrt[6]{2^4}=2^{\frac46}=2^{\frac23}=\sqrt[3]{4}$