For what value of n does open paren 1 over 36 close paren to the n th power is equal to 216 ?

Rewrite both sides using powers of 6: 1/36 = 6⁻² and 216 = 6³. Then (6⁻²)ⁿ = 6⁻²ⁿ, so matching exponents gives −2n = 3. Solving yields n = −3/2, which is choice A, negative 3 halves.

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