We are asked to simplify the expression $\frac{4m^4n^2}{\sqrt{4m^4n^2}}$.

1. Problem Description

We are asked to simplify the expression $\frac{4m^4n^2}{\sqrt{4m^4n^2}}$.

2. Solution Steps

First, we simplify the square root in the denominator:

$\sqrt{4m^4n^2} = \sqrt{4}\sqrt{m^4}\sqrt{n^2} = 2m^2n$

Now, we can rewrite the expression as:

$\frac{4m^4n^2}{2m^2n}$

Next, we simplify the fraction by dividing the coefficients and using the quotient rule for exponents:

$\frac{4}{2} \cdot \frac{m^4}{m^2} \cdot \frac{n^2}{n} = 2 \cdot m^{4-2} \cdot n^{2-1} = 2m^2n$

3. Final Answer

$2m^2n$