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Problem 13 - Entrance Test

If x > 0 and y > 0, which of the following is equivalent to √(x³y⁴) / (x√y)?

Correct: E

√(x³y⁴) / (x√y) = (x^(3/2) * y^(4/2)) / (x * y^(1/2)) = (x^(3/2) * y²) / (x * y^(1/2)) = x^(3/2 - 1) * y^(2 - 1/2) = x^(1/2) * y^(3/2) = x^(1/2) * y * y^(1/2) = y√(xy) = y√x√y. But this doesn't appear to be an option.