Safely. You have correctly chosen the adverb form for independently, so choose the corresponding adverb form for safely. You could instead say helping you have a safer and more independent life .
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BelieverHelping you live safer and more independently.Hi Believer
Helping you live more safely and independently.
I do agree that 'more independently' is correct and to make the overall sentence appear structually sound, it would be better to write it like the second one but the first one doesn't look that bad to me.