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Just tackle the problem in the same way as you would work out a problem in long multiplication and then add up the products as follows:-

C times DLXX = (LVII) => 100*570 = 57,000

XXX times DLXX = (XVII)C => 333*570 = 17,100

V times DLXX = (II)DCCCL => 5*570 = 2,850

III times DLXX = (I)DCCX => 3*570 = 1,710

(LVII)+(XVII)C+(II)DCCCL+(I)DCCX = (LXXVIII)DCLX

57,000+17,100+2,850+1,710 = 78,660

Note that numerals within brackets indicate multiplication by 1,000.

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Q: What is the product of 138 and 570 but showing all work from start to finish in Roman numerals?
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