He answered the question somewhat hastily.
Hastily is the adverb, correctly modifying "answered." How did he answer? Hastily. "Somewhat" is an adverb that is modifying "hastily." How did he answer? Somewhat hastily.
No, because "hasty" is an adjective and would modify a noun. You could say his response was hasty.Would it be?:
He answer the question somewhat hasty.
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