Step 1: Idea:
Break the dance name into parts and see if the parts match the four words in the question.
Step 2: Break the name:
Bharata = Bha + Ra + Ta. Bha stands for bhava (expression), Ra for raga (melody) and Ta for tala (rhythm). The last word natyam means drama or dance drama.
Step 3: Match:
Expression, melody, rhythm and drama are exactly bhava, raga, tala and natyam. No other option name is built this way.
Step 4: Rule out the rest:
Kathak means "story teller". Kathakali means "story play" and stresses drama alone. Manipuri is named after a place, not after these elements. So the answer is option 4.
Final Answer:
The answer is Bharatnatyam.
\[ \boxed{\text{Bharatnatyam}} \]