Which is equivalent to 4th root of 9 raised to the 1 half x power ?

Rewrite the fourth root as an exponent of 1/4. Raising it to the power (1/2)x gives (9^(1/4))^((1/2)x) = 9^((1/4)(1/2)x) = 9^(x/8). So the equivalent expression is 9 raised to the 1/8 x power, choice B.

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