I think this is a question that most pregnant woman wonder about as soon as they find out they are pregnant.  

For the most part, each doctor is different, but first consult with your doctor and get clearance to exercise and perform core exercises.  Once you have clearance, get movin' girlfriend.  Exercise is the best thing you can do for you and your baby.  There are a ton of benefits from exercising during pregnancy.  Click on the following link to see all the benefits of exercising during pregnancy as well as a great thigh and butt prenatal workout:  Benefits of exercise during pregnancy.

As far as should you do core exercises.  ABSOLUTELY!  

SAFE and effective core exercises will help you prevent Diastisis Recti, as well as help you during labor and delivery, prevent low back pain while pregnant and also help you have a flat belly very quickly postpartum.  If that is not reason enough to work your core, I don't know what is.

Now the most effective pregnancy core exercises are ones that work your transverse abdomens.  This is a deep lying muscle in your abdomen and its worked when you do compressions.  For example:  Lie on the floor, legs bent and feet on the floor.  Take a deep breath and let your rib cage and belly expand, and then take one deep exhale and tilt your pelvis and press your belly down.  That is a compression.

There are a ton of great pregnancy core exercises, and today I  am going to give you one AMAZING and super effective pregnancy core exercise.

This is me 32 weeks pregnant!

The BEST Pregnancy Core Exercise:  The CAT:

1. Get in a quadruped position.  Hands and feet touching the floor.
2. Neutral spine.
3. Take one deep breath IN and INHALE as you let your belly drop as far out as you can.
4. Take one deep OUT and as you EXHALE, drive your belly in as far as you can and hold it for a few seconds.
5. Perform 10 repetitions.
6. Slow and controlled movements.

Make sure to work your entire body through weight training and cardio workouts.  If you are unsure of how to perform a safe and effective Pregnancy Workout, click on the following link and I will give you a new pregnancy workout every single month to help you be lean and healthy and energetic throughout your entire pregnancy.  Pregnancy Workouts.

Also, check out what I have to say on CBS NEWS about pregnancy diet and exercise, click here:  pregnancy diet and exercise