To hike up something is to scale or climb it, especially over difficult terrain.
I am not sure whether I am going to hike up to the top of the trail in order to see the waterfall's source, or just stay here and enjoy the view.
I remember when we would hike up to the top of the mountain next to the cabin we stayed at every summer. There was a great place to picnic at the summit.
The expression hike up is also used to mean to raise. For example, one can hike up one’s prices, or raise the prices to a higher level. If you hike up your pants, you pull your the waist of your pants to a higher level.
I hope that you don't plan to hike up your prices for minced beef like all the other markets seem to be doing.
Do you think it is a coincidence that gasoline prices seem to hike up just before the summer driving season begins?
If you raise something, you lift it or move it to a higher position.
In the pioneer times, neighbours would help to build each other's homes and barns, from laying the foundations to raising the roof.
If you raise the expectations in your classroom, I can guarantee you that the students will rise to the occasion.
If you or your actions raise eyebrows, you are doing something that causes others to be shocked or surprised by your actions. Raising eyebrows is usually negative.
What she chose to wear to the charity ball raised eyebrows all over the room, but she did not seem to pay attention.
I think your essay topic is fine, but it may raise eyebrows amongst the more conservative faculty members.