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1 solution
4^n + 1/(4^n) = 7 --> 2^2n + 1/(2^2n) = 7 --> (2^n + 1/(2^n))^2 - 2 = 7 --> 2^n + 1/(2^n) = 3
Therefore, 8ⁿ + 1/8ⁿ = 2^(3n) + 1/(2^3n) = [2^n + 1/(2^n)]^3 - 3(2^n + 1/(2^n)) = 3^3 - 3(3) = 18