If I own a patent, do I have the right to exploit the invention?

No, your patent does not give you the right automatically to practice your own invention - and you certainly do not have the right universally - patents are territorial - each country or group of countries controls the patent rights. The patent gives you the exclusive right to prevent others from making, using, or selling your patented invention but does not give you that right because if you choose to use your patented technology, you may possibly infringe other patents.