Simplify the expression: sqrt(32x4y12 / x8y4)

Here are the solutions to the problems:

1. Simplify the expression: $\sqrt{\frac{32x^4y^{12}}{x^8y^4}}$

Step 1: Simplify the terms inside the square root using exponent rules.

$$\frac{32x^4y^{12}}{x^8y^4} = 32 \cdot x^{4-8} \cdot y^{12-4} = 32x^{-4}y^8 = \frac{32y^8}{x^4}$$

Step 2: Apply the square root to the simplified expression.

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