Which equation is equivalent to 1 third to the x th power is equal to 27 raised to the x plus 2 power ?

Rewrite 1/3 as 3⁻¹, so (1/3)ˣ = 3⁻ˣ. Also, 27 = 3³, so 27^(x + 2) = (3³)^(x + 2) = 3^(3x + 6). Therefore the equivalent equation is 3⁻ˣ = 3^(3x + 6), which is choice C.

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