Remember she is a woman. Don't treat her like she's a buddy and talk man-to-man with a woman who can hold her own and maybe surpass you in conversation. She might know more than you about a topic, but don't force her to show it. Tell her that her thoughts are intriguing and that you love hearing her ideas is just one way to let her know you are aware of her strength and also that you find her very attractive. Don't ask a lot of questions where she has to decide things for you or give you a lot of suggestion. Stay on topics where you can hold your own.
Be the man. Hold open car doors and make sure she feels protected and cared about as you maneuver through your evening together (or whatever time of day it is). Put your hand on her back lightly when crossing the street. Walk on the outside of the curb on the sidewalk. Guide her to a booth or table in a bar or restaurant. Lead, don't follow. She might be used to having to make the decision but i'ts extremely liberating and sexy to be "the girl" and taken care of for the night.
Don't challenge and spar. Many films like to show a smart woman (on the rare occasion they do) as the guy's sidekick or the lead's buddy. And they always are getting and giving out the good lines with the lead guy, making each other feel lower and lower with insults. But that kind of banter is better left for later in the relationship, if at all. A strong woman likes to relax with a man and feel like conversation is easy and gentle, not something where she has to compete.
Kiss her. Take her in your arms and lay one on her if you've gotten signs she'd like that. Be the male in the sexual arena, and don't think that because she's strong she's aggressive sexually. She might be shy and want to be seduced completely.