4 for chest and tris... there is no way you would need to do 4 exercises for each. More is not always better.

I would reccomend doing squats and deads if you're looking to gain overall strength and power... which brings me to my next question:

Are you really looking to gain strength or are you looking to put on size?

You need to read the stickies and read through some of the journals.

IW

strength. i know how to put on size for the most part, but thats the thing. i always look a lot stronger than i actually am. so when you are working out for strength how many times do you work each muscle a week? i was doing everything once. also, seeing it looks like my workout will be shorter going this way, will doing cardio after hurt strength gains? whats a good weekly schedule?

If you want strength then you should not be doing a body part split. That is as the names suggests tailored towards making each body part better (generally: size gain).

For strength I would reccomend a format such as:

3x a week
Week 1: Upper/Lower/Upper
Week 2: Lower/Upper/Lower

or

4x a week
Upper 1, lower 1, Upper 2, Lower 2

or

3x a week full body (this is the way I train)
Mon - Bench, Squats, Rows
Wed - Military Press, Deadlifts, Pull-ups (bicep accessory)
Fri - Decline Bench, Front squats, hams, tricep accessory

Friday we don't usually go ballz out because it is more of a supporting day for the other 2 days.

So, as you can see there are many styles you can train. I have only shown a few.

IW

What about core

Thats something I am working on getting my workout parters to add in and we should be doing it. However, you get excellent core work from any type of squat or deadlift.

IW

any core stabilization stuff you can find....plus anti rotation work.