It helps to write root expressions as rational powers. That is, [tex]\sqrt[n]{x} = x^{\frac1n}[/tex]
Then we have
[tex]\dfrac{\sqrt{4xy^3}}{x^{\frac32} y^{\frac72}} = \sqrt4 \cdot \dfrac{x^{\frac12} y^{\frac32}}{x^{\frac32} y^{\frac72}} = 2x^{\frac12-\frac32} y^{\frac32-\frac72} = 2x^{-1}y^{-2}[/tex]
so that a = 2, b = -1, and c = -2, and thus abc = 4.
