Simplify the polynomial expression. (64x^8y^12)^(1)/(2)

To simplify the polynomial expression $(64x^{8}y^{12})^{\frac{1}{2}}$, we can use the properties of exponents and radicals.

First, let's rewrite the expression inside the parentheses:
$$(64x^{8}y^{12})^{\frac{1}{2}}$$

We can distribute the exponent $\frac{1}{2}$ to each term inside the parentheses:
$$= 64^{\frac{1}{2}} \cdot (x^{8})^{\frac{1}{2}} \cdot (y^{12})^{\frac{1}{2}}$$

Now, let's simplify each term separately:

1. $64^{\frac{1}{2}}$:
$$64^{\frac{1}{2}} = \sqrt{64} = 8$$

2. $(x^{8})^{\frac{1}{2}}$:
$$(x^{8})^{\frac{1}{2}} = x^{8 \cdot \frac{1}{2}} = x^{4}$$

3. $(y^{12})^{\frac{1}{2}}$:
$$(y^{12})^{\frac{1}{2}} = y^{12 \cdot \frac{1}{2}} = y^{6}$$

Now, we combine these simplified terms:
$$8 \cdot x^{4} \cdot y^{6}$$

Therefore, the simplified form of the polynomial expression $(64x^{8}y^{12})^{\frac{1}{2}}$ is:
$$8x^{4}y^{6}$$