my 10 year old step son has starting putting on a little babies voice in order to get his own way...?

Don't give into your child getting his way because that could make the situation worse as the child ages. If you give in now, the child will think that talking in a baby voice is okay. Your child is young so stopping this behavior using a slow and nonjudgmental process is alright; just try not to hurt his feelings. Both parents have to be consistent in parenting and with what they say. If the mother tells the son that he can't speak in this babies voice, then the father should say that too. Just be consistent and take this one step at a time. Eventually, your child will grow out of the phase of speaking like a child... Very soon.

the simple way for you to deal with it is by not responding to anything said in the baby voice---- you only hear him when he speaks properly. that does not however address the emotional issues that are causing the behavior.

I would guess he would likes to be coddled a bit, perhaps because he is stressed by dad. If he were my son, I would give him a hug or cuddle or word of praise every chance appropriate, esp if I were responding to something he said o asked in age appropriate voice.

Don't respond or just say "no" in a teeny tiny voice. tell him if he needs some attention to talk with his ten year old voice.

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