we will do the excrises as soon as possible. 用法对吗？

完全正确

你好

冠词the使用错误，锻炼应该为do excrises
去掉the
we will do excrises as soon as possible.

we will do excrises as soon as possible

不对，应该去掉冠词the，We will do exercise as soon as possible(我们会尽快的做运动)。

这句话完全正确。
as soon as possible，搭配，尽可能快。
翻译：我们将尽可能快地完成练习。