For what value of n does the fraction with numerator 216 raised to the n minus 2 power and denominator open paren 1 over 36 close paren raised to the 3 n power is equal to 216 ?

Rewrite both numbers using base 6: 216 = 6³ and 1/36 = 6⁻². Dividing by (1/36)³ⁿ is the same as multiplying by 6⁶ⁿ, so the fraction becomes 6^[3(n − 2) + 6n] = 6^(9n − 6). Since it equals 216 = 6³, set 9n − 6 = 3, which gives n = 1. The correct choice is A, 1.

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