Nuclear Power in Space, beamed down by laser

You know, I've had this thought before, but I have no training, nothing of the sort in engineering, nothing. I reserve the right to be a complete idiot in this blog post.  I don't know shit about this.

Wouldn't nuclear power be safe in space?  Couldn't lasers transmit the energy? Hopefully the lasers themselves wouldn't fry the atmosphere...

I know that nuclear power can basically be forever, I know that it's incredibly dangerous to our biosphere, but that we have the ability to operate beyond our biosphere.  Wouldn't nuclear be safe out in space?  Wouldn't the only trick be the transmission of energy to collection stations?

So why not get our energy from safe nuclear? Safe means outside the atmosphere.

I have no idea if anyone's thought about this before, wouldn't be surprised if it's a standard trope by sci fi authors, and Not My Job to work out the details. I have nothing of value to contribute to any comments.

May anyone who sees this smile. 

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I do know I gain brain energy from considering the image.  Imagery is the first language of humans, the true conduit between the body and the mind.