They did the experiment as their chemistry teacher had instructed.

划线部分为“方式状语从句”。

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 as you were told. 

等于：Do it as 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。