Even before this God displays His plan by making sure Moses goes to Pharaoh. If you recall Moses is called by God, and yet comes up with excuse after excuse to not go to Egypt. God continues to counter those excuses until Moses has none. And then he goes to Egypt and begins pleading for the people of Israel.
Back to the plagues. In Exodus 9:15-16, I believe, we see clearly God's power and plan declared. I hope you see this. His power is declared in verse 15. His plan is declared in verse 16.
(15) For by now I could have put out my hand and struck you and your people with pestilence, and you would have been cut off from the earth.From this verse I can see clearly God's power. He states that He 'could have' put out His hand and struck the Egyptians (talking specifically to Pharaoh). If God decided to do this the result would be that they would have been cut off from the earth! Surely our God has great power.
(16) But for this purpose I have raised you up, to show you my power, so that my name may be proclaimed in all the earth.From this verse I see God's plan. God raised Pharaoh up for the purpose of God's name being proclaimed in all the earth. That was Pharaoh's purpose. And the all-powerful God of the universe will accomplish His purose.