To Exert
To Reach To
transitive verb, godan verb
If 及ぶ is "to reach" then this is something similar. Now you're doing the reaching, and to reach something you have to exert yourself to do it. Also, you have to reach to the goal you're trying to reach.
およぼす
The reading comes from 及ぶ, so if you know that, you'll reach the ability to know this word's reading as well.
放射能汚染は人体にどのような影響を及ぼすと考えられているのでしょうか。
What effect do people think radioactive contamination has on the human body?