a)\(\sqrt{4x^2}\cdot\sqrt{\dfrac{9}{x^4y^2}}=\sqrt{\left(2x\right)^2}\cdot\dfrac{\sqrt{3^2}}{\sqrt{\left(x^2y\right)^2}}\)
\(=\left|2x\right|\cdot\dfrac{3}{\left|x^2y\right|}=\dfrac{6x}{x^2y}=\dfrac{6}{xy}\left(x;y>0\right)\)
b)\(\sqrt{a}\cdot\sqrt{2a}\cdot\sqrt{\dfrac{4}{a^4}}=\sqrt{2a^2}\cdot\dfrac{\sqrt{4}}{\sqrt{a^4}}=\dfrac{\sqrt{8a^2}}{\sqrt{a^4}}\)
\(=\dfrac{\sqrt{8}}{\sqrt{a^2}}=\dfrac{2\sqrt{2}}{\left|a\right|}=\dfrac{2\sqrt{2}}{a}\left(a>0\right)\)
a: \(=\sqrt{4x^2\cdot\dfrac{9}{x^4y^2}}=\sqrt{\dfrac{36}{x^2y^2}}=\dfrac{6}{xy}\)
b: \(=\sqrt{2a\cdot a\cdot\dfrac{4}{a^4}}=\sqrt{\dfrac{8}{a^2}}=\dfrac{2\sqrt{2}}{a}\)
