Training for your arms and legs is essential to developing powerful punches and kicks for MMA, but it is core strength that will give you the advantage over an opponent who is lacking in this area.
Some key MMA-specific reasons for a strong core:

• You'll sustain stability and put more force behind kicks and punches throughout an entire fight.
• You will be better able to get out of a hold or reverse your opponent's advantage on the ground.
• You will be better able to execute clinch moves to hold the dominant position on the ground.
• You will have more power behind every move.

In addition, a strong core protects your back from injury and improves posture and circulation, both of which help you train harder and safer.