This question is quite easy if you've memorized your powers, specifically the powers of 3. When you recognize that 27 = 3^3, and 81 = 3^4, you can convert quantity A as follows:
27^8 = (3^3)^8 = 3^24
since powers in parenthesis can be multiplied. Similarly, quantity B can be converted as follows:
81^6 = (3^4)^6 = 3^24
Thus, the two quantities are equal, so it's C.
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