Is Nuclear Power Really Safe?

Recently, I have heard a lot of conservatives talking about how "safe" nuclear power is. Is it possible that they don't remember the nuclear-meltdown that is still affecting the Town of Chernobyl? They don't remember the Three-Mile Island debacle? Can it be that they never head about what happened in Japan a number of years back? Nuclear power is not safe--it has never been, and never will be safe to use on Earth, because there is no way to dispose of the radioactive waste which results from nuclear fission.
However, nuclear power could be safely used in space. Space is already radioactive, so there would be no harm from the radioactive by-products that result from generating nuclear power in space. Nuclear waste could be fired out of the solar-system or into the Sun, and it wouldn't hurt anybody. The energy generated by nuclear reactors (or solar panels) in space could then be be transmitted to a receiving station on Earth, via microwave. The result would be clean, cheap, and plentiful energy for the entire planet.