My personal opinion on the omnipotence of God is that in realm of all that is possible for man or God to accomplish, God is able to do all things that fall into that realm of possibility. However, I do believe that there are certain things that are infinitely impossible that cannot be done, not even by God Himself. This is primarily based on Latter-day scripture given by the Prophet Joseph Smith. I don't believe that God can create something out of absolute nothingness. I believe that the elements are eternal and also the intelligence of all living things are self existent and cannot be created or made by God. Mankind, I believe doesn't even come close to knowing all things that are possible with God or what may be impossible for God. We only have revelation from God which gives us light and knowledge as to what things are eternally impossible with God and what things are truly possible for God. So, for these reasons, I believe that in the realm of all that is possible in all existence, God is all powerful to do all things that are possible. However, I do believe that with God there are eternal impossabilites that not even God can do. I certainly don't believe that God can exist and not exist simultaneously.