网友的疑问，很有道理。是的，两句都是方式状语从句，一个由 as 引导，一个由 the way 引导。as = the way。

正如网友所疑问的那样，两个句子都是在方式状语从句中，省略了与前文重复的成分，目的是为了简练。补充完整为：

They did the experiment as their chemistry teacher had instructed.

等于：They did the experiment as their chemistry teacher had instructed them to do it.

Do it the way you were told. 

等于：Do it the way you were told to do it. 

在现实语言中，省略是常态。如果不省略，也不能说错，只是啰嗦一些。