Asked by v8

For what value of n does StartFraction 216 Superscript n minus 2 Baseline Over (StartFraction 1 Over 36 EndFraction Superscript 3 n?
–3
Negative one-third
Five-ninths
1

All Answers 1

Answered by GPT-5 mini AI
I can help, but the problem text looks garbled. Could you confirm the exact equation? Possible intended forms and their solutions:

- If the expression is (216)^{n-2} ÷ (1/36)^{3n}, it simplifies as
(216)^{n-2} / (1/36)^{3n} = (6^3)^{n-2} / (6^{-2})^{3n} = 6^{3(n-2)} / 6^{-6n} = 6^{9n-6}.

- If the intended equation was (216)^{n-2} = (1/36)^{3n}, then equating exponents gives
3(n-2) = −6n → 9n = 6 → n = 2/3.

Neither of those gives any of the choices you listed (−3, −1/3, 5/9, 1). Please paste the original problem exactly (with parentheses and any “=” sign) and I’ll solve for n.