1. **State the problem:** Simplify the expression $$\sqrt{\frac{4x^2}{9y^4}}$$ and verify if it equals $$\frac{8}{3xy}$$. 2. **Recall the formula:** The square root of a fraction is the fraction of the square roots: $$\sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}}$$ 3. **Check if the numerator and denominator are perfect squares:** - Numerator: $$4x^2 = (2x)^2$$, which is a perfect square. - Denominator: $$9y^4 = (3y^2)^2$$, which is also a perfect square. 4. **Simplify the square root:** $$\sqrt{\frac{4x^2}{9y^4}} = \frac{\sqrt{4x^2}}{\sqrt{9y^4}} = \frac{2x}{3y^2}$$ 5. **Compare with the given expression:** The expression $$\frac{8}{3xy}$$ is not equal to $$\frac{2x}{3y^2}$$. 6. **Conclusion:** The simplified form of $$\sqrt{\frac{4x^2}{9y^4}}$$ is $$\frac{2x}{3y^2}$$, which does not match any of the options a), b), c), or d). **Final answer:** $$\frac{2x}{3y^2}$$