Can we replace deterministic part of alternative turing machine with some other equivalent machines? I'm sorry if it is a low level question but I am so confusing.

If $DTime(n)\subseteq \Sigma_2Time(n^{0.2})$ then $DTime(n) \subseteq \Sigma_2DTime(n^{0.2})$ 

Is this true that $\Sigma_2DTime(n^{0.2})\subseteq\Sigma_2\Sigma_2Time((n^{0.2})^{0.2})=\Sigma_4Time(n^{0.04})$

I picked up DTime in alternative machine and replaced it with $DTime(n)\subseteq \Sigma_2Time(n^{0.2})$  and replacing  n with $n^{0.2}$.
I think you need to work on what $(0.2)^2$ is before you go any further.