Simplify the numerator 9^(1)/(2).

A fractional exponent of $\frac{1}{2}$ means taking the square root.

$$9^{\frac{1}{2}} = \sqrt{9} = 3$$

A fractional exponent of $\frac{2}{3}$ means taking the cube root and then squaring the result.

$$27^{\frac{2}{3}} = (\sqrt[3]{27})^2$$

First, find the cube root of 27:

$$\sqrt[3]{27} = 3 \quad \text{since } 3 \times 3 \times 3 = 27$$

Now, square the result:

$$3^2 = 9$$

So, $27^{\frac{2}{3}} = 9$.

$$\frac{3}{9} = \frac{1}{3}$$

The simplified expression is $\frac{1}{3}$. This matches option B.

The final answer is $\text{B. } \frac{1}{3}$.